•Download as PPTX, PDF•

1 like•386 views

The document discusses factoring perfect square trinomials. It defines a perfect square trinomial as having the first and last terms as perfect squares, and the middle term twice the product of the first and last terms. The document provides examples of factoring perfect square trinomials using the multiplication breaker map (MBM) method. This involves taking the square root of the first and last terms, checking if the middle term satisfies the definition, and then factoring the expression as the sum or difference of the two terms squared. The document concludes with an activity having students work in groups to factor various perfect square trinomials using MBM.

Report

Share

Report

Share

Factoring Sum and Difference of Two Cubes

This will help you in factoring sum and difference of two cubes.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

Factoring Polynomials

This document provides instructions on factoring polynomials of various forms:
1) It explains how to factor polynomials by finding the greatest common factor (GCF).
2) It describes how to factor trinomials of the form x2 + bx + c by finding two numbers whose sum is b and product is c.
3) It shows how to factor trinomials of the form ax2 + bx + c by finding factors of a, c whose products and sums satisfy the polynomial.

Geometric sequences

This document discusses geometric sequences, which are sequences where each term is found by multiplying the preceding term by a constant ratio. It provides the recursive and explicit forms for writing geometric sequences, and gives examples of finding specific terms and writing the explicit formula given the first term and ratio. Key details include that the recursive form is an+1 = ar, and the explicit form is an = arn-1, where a is the first term and r is the common ratio.

Lesson 1: Special Products

This document provides examples and rules for working with exponents and polynomials. It begins by showing the step-by-step working of three multiplication problems involving exponents. It then states the product rule for exponents and the rule for raising a power to another power. The document encourages positive thinking and hard work. It ends by having the reader say a phrase aloud together to reinforce a growth mindset towards math.

Factoring Perfect Square Trinomials Worksheet

This document is a mathematics worksheet on algebra that provides instructions on factoring perfect square trinomials. It explains that recognizing the pattern of perfect squares can save time on tests. The pattern is to take the square roots of the first and last terms and place them in parentheses with a plus or minus between them, then square the whole expression. Examples of factoring expressions using this pattern are provided.

Addition and subtraction of rational expression

To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.

Factoring Perfect Square Trinomial

The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.

Multiplying & dividing rational algebraic expressions

This document discusses how to multiply and divide rational algebraic expressions. It explains that to multiply rational expressions, one multiplies the numerators and denominators separately. Rational expressions must first be factored to cancel common factors before multiplying. Several examples of multiplying rational expressions are shown. The document also explains that to divide rational expressions, one multiplies the numerator by the reciprocal of the denominator. Some examples of dividing rational expressions are provided.

Factoring Sum and Difference of Two Cubes

This will help you in factoring sum and difference of two cubes.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

Factoring Polynomials

This document provides instructions on factoring polynomials of various forms:
1) It explains how to factor polynomials by finding the greatest common factor (GCF).
2) It describes how to factor trinomials of the form x2 + bx + c by finding two numbers whose sum is b and product is c.
3) It shows how to factor trinomials of the form ax2 + bx + c by finding factors of a, c whose products and sums satisfy the polynomial.

Geometric sequences

This document discusses geometric sequences, which are sequences where each term is found by multiplying the preceding term by a constant ratio. It provides the recursive and explicit forms for writing geometric sequences, and gives examples of finding specific terms and writing the explicit formula given the first term and ratio. Key details include that the recursive form is an+1 = ar, and the explicit form is an = arn-1, where a is the first term and r is the common ratio.

Lesson 1: Special Products

This document provides examples and rules for working with exponents and polynomials. It begins by showing the step-by-step working of three multiplication problems involving exponents. It then states the product rule for exponents and the rule for raising a power to another power. The document encourages positive thinking and hard work. It ends by having the reader say a phrase aloud together to reinforce a growth mindset towards math.

Factoring Perfect Square Trinomials Worksheet

This document is a mathematics worksheet on algebra that provides instructions on factoring perfect square trinomials. It explains that recognizing the pattern of perfect squares can save time on tests. The pattern is to take the square roots of the first and last terms and place them in parentheses with a plus or minus between them, then square the whole expression. Examples of factoring expressions using this pattern are provided.

Addition and subtraction of rational expression

To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.

Factoring Perfect Square Trinomial

The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.

Multiplying & dividing rational algebraic expressions

This document discusses how to multiply and divide rational algebraic expressions. It explains that to multiply rational expressions, one multiplies the numerators and denominators separately. Rational expressions must first be factored to cancel common factors before multiplying. Several examples of multiplying rational expressions are shown. The document also explains that to divide rational expressions, one multiplies the numerator by the reciprocal of the denominator. Some examples of dividing rational expressions are provided.

Dividing Polynomials Slide Share

I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...

Lesson plan on factoring polynomial with common monomial factor

The document is a lesson plan for teaching factoring polynomials with common monomial factors in Math 8. It includes the intended learning outcomes, which are for students to define and apply common monomial factoring. The lesson content discusses factoring polynomials through finding the greatest common factor. Examples are provided to demonstrate finding the GCF and factoring polynomials. Students will complete an activity identifying common factors in pictures and practice problems are assigned to reinforce the skill.

Linear Equations in Two Variables

The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.

7.8.-SPECIAL-PRODUCTS.ppt

This document discusses special products of binomials, including:
- (a + b)2 = a2 + 2ab + b2, known as a perfect-square trinomial
- (a - b)2 = a2 - 2ab + b2, also a perfect-square trinomial
- (a + b)(a - b) = a2 - b2, known as the difference of two squares
It provides examples of using these rules to simplify expressions involving binomials squared or multiplied together.

Factoring the Difference of Two Squares Worksheet

This mathematics worksheet provides 20 practice problems for factoring the difference of two squares using the identity x^2 - y^2 = (x + y)(x - y). The worksheet includes the factorizations of algebraic expressions involving variables like x, y, a, b, c, d, e, m, n, p, and q. It also provides the student's name, grade/section, date, and score at the top for identification and grading purposes.

Adding and subtracting rational expressions

Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.

Graphs of polynomial functions

The document summarizes key characteristics of polynomial functions:
1) Polynomial functions produce smooth, continuous curves on their domains which are the set of real numbers.
2) The graph's x-intercepts, turning points, and absolute/relative maxima and minima are defined.
3) As the degree of a polynomial increases, so do the possible number of x-intercepts and turning points, up to the degree value. The leading coefficient and degree determine whether the graph rises or falls.

Factoring The Sum and Difference of Two Cubes

1. The lesson plan is for a math class on factoring the sum and difference of two cubes.
2. Students will do an activity matching cube root terms to images to help understand getting cube roots and the patterns in factoring sums and differences of cubes.
3. The lesson will review getting cube roots, then demonstrate the steps to factor sums and differences of cubes by getting the cube root of each term, forming a binomial, and using the binomial to factor the expression. Students will do examples to practice.

Grade 8 Mathematics Common Monomial Factoring

The document provides instructions for an individual activity where students must follow 16 directions within 2 minutes to complete tasks like writing their name, drawing shapes, and tapping their desk. It asks what implications the activity might have if directions are not followed properly. The second part of the document provides examples of factoring polynomials using greatest common factor and common monomial factoring methods. It includes practice problems for students to determine the greatest common factor, quotient, and factored form. The document emphasizes following directions and learning different factoring techniques.

writing linear equation

This document provides examples for rewriting linear equations between the slope-intercept form (y=mx+b) and standard form (Ax + By = C).
It begins with examples of rewriting equations from standard form to slope-intercept form and identifying the slope (m) and y-intercept (b). Then it provides examples of rewriting from slope-intercept form to standard form. Finally, it provides a series of practice problems for rewriting linear equations between the two forms.

Factoring the Difference of Two Squares

The document discusses factoring the difference of two squares. It involves reviewing factoring the difference of two squares, which involves recognizing that the difference of two squares can be written as the product of two binomials, where one binomial contains the sum of the two terms and the other contains their difference.

Adding and subtracting rational expressions with different denominator

The document outlines a lesson plan for teaching students how to add and subtract rational expressions with different denominators, including identifying the least common denominator, combining like terms, and simplifying rational expressions. Sample problems are provided demonstrating how to find the least common denominator and perform the indicated operations on rational expressions with different variables in the denominators. A homework assignment is given asking students to reflect on what they learned about adding and subtracting rational expressions.

Math Performance task (2nd quarter)

The document analyzes the costs of owning and operating two used cars, Car A and Car B, over a 2-year period. Car B has higher fuel efficiency at 35 km per gallon compared to Car A's 20 km per gallon, resulting in lower estimated fuel costs of ₱57,600 over 2 years for Car B versus ₱100,800 for Car A, making Car B the more economical choice. However, the document also notes that brand, style and status may be more important factors for some buyers, so either car could be suitable depending on the consumer's preferences and financial situation.

Polynomials

The document defines key polynomial vocabulary including:
- Terms are numbers or products of numbers and variables raised to powers. Coefficients are numerical factors of terms. Constants are terms that are only numbers.
- Polynomials are sums of terms involving variables raised to whole number exponents, with no variables in denominators.
- Types of polynomials include monomials (1 term), binomials (2 terms), and trinomials (3 terms). Degree is the largest exponent of any term.
- Operations on polynomials include adding/subtracting like terms, multiplying using distribution and FOIL, dividing using long division, and special products like (a+b)2 and (a+b)(a

Factoring Perfect Square Trinomial

1. The document is a lesson plan for teaching factoring perfect square trinomials in Math 8. It includes intended learning outcomes, learning content on factoring perfect square trinomials, sample learning activities involving tiles, and examples to factor.
2. Students will factor perfect square trinomials and find square roots. Learning activities involve using tiles to form squares and noticing patterns. Examples are provided to demonstrate factoring trinomials by getting square roots and forming sums or differences.
3. An evaluation section includes more examples for students to factor completely to check their understanding of factoring perfect square trinomials.

perfect square trinomial

This document provides guidance on identifying and factoring perfect square trinomials in algebra. It begins with a definition of a perfect square trinomial as a trinomial that results from squaring a binomial. Examples are provided to illustrate this. Several activity cards are then presented to help students practice determining if an expression is a perfect square trinomial, completing the terms, factoring, and more. An enrichment card adds an assessment with multiple choice questions. Key steps for factoring a perfect square trinomial are outlined, such as taking the square root of the first and last terms. An answer card provides the solutions to the activities. Sources are listed at the end.

Cartesian coordinate plane

The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin (0,0). It describes how each point on the plane is associated with an ordered pair (x,y) denoting its coordinates and how the plane is divided into four quadrants. It then demonstrates how to plot various points on the plane by starting at the origin and moving right or left along the x-axis and up or down along the y-axis. Finally, it discusses relations and functions, defining a function as a relation where each x-value is mapped to only one y-value.

Cube of binomial

The cube of a binomial can be found using the formula F3 + 3F2L + 3FL2 + L3, where:
- F3 is the cube of the first term
- 3F2L is 3 times the square of the first term multiplied by the second term
- 3FL2 is 3 times the first term multiplied by the square of the second term
- L3 is the cube of the second term
This formula is demonstrated through examples of finding the cubes of (x + 2), (x - 2), and (2x + y).

Trigonometry - The Six Trigonometric Ratios

This document discusses trigonometry and its key concepts. It defines trigonometry as a branch of mathematics concerning the study of triangles and the relationship between side lengths and angles. It notes that Hipparchus of Nicaea in the 2nd century BC is considered the father of trigonometry. The document outlines important trigonometric ratios like sine, cosine and tangent, and defines concepts like adjacent, opposite, and hypotenuse sides of a right triangle. It also discusses Pythagoras' theorem relating side lengths in a right triangle.

Polynomial equations

Here are the remainders when dividing the given polynomials by the specified polynomials:
1. The remainder is 0. Therefore, x-1 is a factor of x3+3x2-4x+2.
2. The remainder is 5.
3. The remainder is 0. Therefore, x+2 is a factor of 2x3+5x2+3x+11.
4. The remainder is 4.
5. The remainder is 7.
6. The remainder is 2.

Factoring Polynomials in Modular Approach

The document provides lessons on factoring polynomials with common monomial factors and the difference of two squares. It explains that to factor polynomials with common monomial factors, one must find the greatest common factor (GCF) and divide each term by the GCF. It also explains that to factor the difference of two squares, one must get the square root of each term and use those roots to form the sum and difference as factors. Examples are provided to demonstrate these factoring techniques step-by-step. The document aims to teach learners how to completely factor different types of polynomials.

Factoring Strategies

Happy Math Humans (group h) of 8 - St. Basil
3 students of 8 - St. Basil representing the group Happy Math Humans, will show you how to factor different types of polynomials.

Dividing Polynomials Slide Share

I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...

Lesson plan on factoring polynomial with common monomial factor

The document is a lesson plan for teaching factoring polynomials with common monomial factors in Math 8. It includes the intended learning outcomes, which are for students to define and apply common monomial factoring. The lesson content discusses factoring polynomials through finding the greatest common factor. Examples are provided to demonstrate finding the GCF and factoring polynomials. Students will complete an activity identifying common factors in pictures and practice problems are assigned to reinforce the skill.

Linear Equations in Two Variables

The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.

7.8.-SPECIAL-PRODUCTS.ppt

This document discusses special products of binomials, including:
- (a + b)2 = a2 + 2ab + b2, known as a perfect-square trinomial
- (a - b)2 = a2 - 2ab + b2, also a perfect-square trinomial
- (a + b)(a - b) = a2 - b2, known as the difference of two squares
It provides examples of using these rules to simplify expressions involving binomials squared or multiplied together.

Factoring the Difference of Two Squares Worksheet

This mathematics worksheet provides 20 practice problems for factoring the difference of two squares using the identity x^2 - y^2 = (x + y)(x - y). The worksheet includes the factorizations of algebraic expressions involving variables like x, y, a, b, c, d, e, m, n, p, and q. It also provides the student's name, grade/section, date, and score at the top for identification and grading purposes.

Adding and subtracting rational expressions

Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.

Graphs of polynomial functions

The document summarizes key characteristics of polynomial functions:
1) Polynomial functions produce smooth, continuous curves on their domains which are the set of real numbers.
2) The graph's x-intercepts, turning points, and absolute/relative maxima and minima are defined.
3) As the degree of a polynomial increases, so do the possible number of x-intercepts and turning points, up to the degree value. The leading coefficient and degree determine whether the graph rises or falls.

Factoring The Sum and Difference of Two Cubes

1. The lesson plan is for a math class on factoring the sum and difference of two cubes.
2. Students will do an activity matching cube root terms to images to help understand getting cube roots and the patterns in factoring sums and differences of cubes.
3. The lesson will review getting cube roots, then demonstrate the steps to factor sums and differences of cubes by getting the cube root of each term, forming a binomial, and using the binomial to factor the expression. Students will do examples to practice.

Grade 8 Mathematics Common Monomial Factoring

The document provides instructions for an individual activity where students must follow 16 directions within 2 minutes to complete tasks like writing their name, drawing shapes, and tapping their desk. It asks what implications the activity might have if directions are not followed properly. The second part of the document provides examples of factoring polynomials using greatest common factor and common monomial factoring methods. It includes practice problems for students to determine the greatest common factor, quotient, and factored form. The document emphasizes following directions and learning different factoring techniques.

writing linear equation

This document provides examples for rewriting linear equations between the slope-intercept form (y=mx+b) and standard form (Ax + By = C).
It begins with examples of rewriting equations from standard form to slope-intercept form and identifying the slope (m) and y-intercept (b). Then it provides examples of rewriting from slope-intercept form to standard form. Finally, it provides a series of practice problems for rewriting linear equations between the two forms.

Factoring the Difference of Two Squares

The document discusses factoring the difference of two squares. It involves reviewing factoring the difference of two squares, which involves recognizing that the difference of two squares can be written as the product of two binomials, where one binomial contains the sum of the two terms and the other contains their difference.

Adding and subtracting rational expressions with different denominator

The document outlines a lesson plan for teaching students how to add and subtract rational expressions with different denominators, including identifying the least common denominator, combining like terms, and simplifying rational expressions. Sample problems are provided demonstrating how to find the least common denominator and perform the indicated operations on rational expressions with different variables in the denominators. A homework assignment is given asking students to reflect on what they learned about adding and subtracting rational expressions.

Math Performance task (2nd quarter)

The document analyzes the costs of owning and operating two used cars, Car A and Car B, over a 2-year period. Car B has higher fuel efficiency at 35 km per gallon compared to Car A's 20 km per gallon, resulting in lower estimated fuel costs of ₱57,600 over 2 years for Car B versus ₱100,800 for Car A, making Car B the more economical choice. However, the document also notes that brand, style and status may be more important factors for some buyers, so either car could be suitable depending on the consumer's preferences and financial situation.

Polynomials

The document defines key polynomial vocabulary including:
- Terms are numbers or products of numbers and variables raised to powers. Coefficients are numerical factors of terms. Constants are terms that are only numbers.
- Polynomials are sums of terms involving variables raised to whole number exponents, with no variables in denominators.
- Types of polynomials include monomials (1 term), binomials (2 terms), and trinomials (3 terms). Degree is the largest exponent of any term.
- Operations on polynomials include adding/subtracting like terms, multiplying using distribution and FOIL, dividing using long division, and special products like (a+b)2 and (a+b)(a

Factoring Perfect Square Trinomial

1. The document is a lesson plan for teaching factoring perfect square trinomials in Math 8. It includes intended learning outcomes, learning content on factoring perfect square trinomials, sample learning activities involving tiles, and examples to factor.
2. Students will factor perfect square trinomials and find square roots. Learning activities involve using tiles to form squares and noticing patterns. Examples are provided to demonstrate factoring trinomials by getting square roots and forming sums or differences.
3. An evaluation section includes more examples for students to factor completely to check their understanding of factoring perfect square trinomials.

perfect square trinomial

This document provides guidance on identifying and factoring perfect square trinomials in algebra. It begins with a definition of a perfect square trinomial as a trinomial that results from squaring a binomial. Examples are provided to illustrate this. Several activity cards are then presented to help students practice determining if an expression is a perfect square trinomial, completing the terms, factoring, and more. An enrichment card adds an assessment with multiple choice questions. Key steps for factoring a perfect square trinomial are outlined, such as taking the square root of the first and last terms. An answer card provides the solutions to the activities. Sources are listed at the end.

Cartesian coordinate plane

The document discusses the Cartesian coordinate plane and functions. It defines the Cartesian plane as being formed by two perpendicular number lines called the x-axis and y-axis that intersect at the origin (0,0). It describes how each point on the plane is associated with an ordered pair (x,y) denoting its coordinates and how the plane is divided into four quadrants. It then demonstrates how to plot various points on the plane by starting at the origin and moving right or left along the x-axis and up or down along the y-axis. Finally, it discusses relations and functions, defining a function as a relation where each x-value is mapped to only one y-value.

Cube of binomial

The cube of a binomial can be found using the formula F3 + 3F2L + 3FL2 + L3, where:
- F3 is the cube of the first term
- 3F2L is 3 times the square of the first term multiplied by the second term
- 3FL2 is 3 times the first term multiplied by the square of the second term
- L3 is the cube of the second term
This formula is demonstrated through examples of finding the cubes of (x + 2), (x - 2), and (2x + y).

Trigonometry - The Six Trigonometric Ratios

This document discusses trigonometry and its key concepts. It defines trigonometry as a branch of mathematics concerning the study of triangles and the relationship between side lengths and angles. It notes that Hipparchus of Nicaea in the 2nd century BC is considered the father of trigonometry. The document outlines important trigonometric ratios like sine, cosine and tangent, and defines concepts like adjacent, opposite, and hypotenuse sides of a right triangle. It also discusses Pythagoras' theorem relating side lengths in a right triangle.

Polynomial equations

Here are the remainders when dividing the given polynomials by the specified polynomials:
1. The remainder is 0. Therefore, x-1 is a factor of x3+3x2-4x+2.
2. The remainder is 5.
3. The remainder is 0. Therefore, x+2 is a factor of 2x3+5x2+3x+11.
4. The remainder is 4.
5. The remainder is 7.
6. The remainder is 2.

Dividing Polynomials Slide Share

Dividing Polynomials Slide Share

Lesson plan on factoring polynomial with common monomial factor

Lesson plan on factoring polynomial with common monomial factor

Linear Equations in Two Variables

Linear Equations in Two Variables

7.8.-SPECIAL-PRODUCTS.ppt

7.8.-SPECIAL-PRODUCTS.ppt

Factoring the Difference of Two Squares Worksheet

Factoring the Difference of Two Squares Worksheet

Adding and subtracting rational expressions

Adding and subtracting rational expressions

Graphs of polynomial functions

Graphs of polynomial functions

Factoring The Sum and Difference of Two Cubes

Factoring The Sum and Difference of Two Cubes

Grade 8 Mathematics Common Monomial Factoring

Grade 8 Mathematics Common Monomial Factoring

writing linear equation

writing linear equation

Factoring the Difference of Two Squares

Factoring the Difference of Two Squares

Adding and subtracting rational expressions with different denominator

Adding and subtracting rational expressions with different denominator

Math Performance task (2nd quarter)

Math Performance task (2nd quarter)

Polynomials

Polynomials

Factoring Perfect Square Trinomial

Factoring Perfect Square Trinomial

perfect square trinomial

perfect square trinomial

Cartesian coordinate plane

Cartesian coordinate plane

Cube of binomial

Cube of binomial

Trigonometry - The Six Trigonometric Ratios

Trigonometry - The Six Trigonometric Ratios

Polynomial equations

Polynomial equations

Factoring Polynomials in Modular Approach

The document provides lessons on factoring polynomials with common monomial factors and the difference of two squares. It explains that to factor polynomials with common monomial factors, one must find the greatest common factor (GCF) and divide each term by the GCF. It also explains that to factor the difference of two squares, one must get the square root of each term and use those roots to form the sum and difference as factors. Examples are provided to demonstrate these factoring techniques step-by-step. The document aims to teach learners how to completely factor different types of polynomials.

Factoring Strategies

Happy Math Humans (group h) of 8 - St. Basil
3 students of 8 - St. Basil representing the group Happy Math Humans, will show you how to factor different types of polynomials.

Tema# 2 Repaso de factorización

This document provides a guide for factorizing algebraic expressions. It begins with definitions of factorizing and factoring common terms. It then covers various factoring methods including: factoring a common monomial, factorizing a common polynomial, factoring by grouping terms, factoring a perfect square trinomial, factoring the difference of squares, factoring a trinomial in the form x^2 + bx + c, factoring a trinomial with a coefficient on the x^2 term, factoring the difference of cubes, and challenges for students to practice these methods. The document is intended as a review for students to study factorizing skills.

March 23, 2015

The document outlines a lesson on factoring polynomials, including reviewing factoring perfect square trinomials and introducing methods for factoring general trinomials of the form ax^2 + bx + c, such as grouping, the box method, and trial and error. It also notes an upcoming factoring test and provides examples and notes for students to complete as class work.

Math Q1 - Week 2.pdf

The document provides a lesson on factoring the sum and difference of two cubes. It begins with definitions of perfect cubes and examples of factoring expressions like x3 - 27 and x3 + 27 using the rule that (x - a)(x2 + ax + a2) = x3 - a3 and (x + a)(x2 - ax + a2) = x3 + a3. Students are then asked to determine if additional expressions are the sum or difference of two cubes and factor them accordingly. The next section covers factoring perfect square trinomials, defining them as expressions of the form a2 + 2ab + b2 and providing the factoring pattern (a + b)2. Examples

Q1-W1-Factoring Polynomials.pptx

This document provides instruction on factoring polynomials. It covers several factoring methods including common monomial factoring, difference of squares, sum and difference of cubes, perfect square trinomials, and general trinomials. Examples are provided for each method. The objectives are to determine appropriate factoring methods, factor polynomials completely using various techniques, and solve problems involving polynomial factors.

Factoring Polynomials with Common Monomial Factor.pptx

The document discusses factoring polynomials. It covers 7 techniques for factoring different types of polynomials, including those with a common monomial factor. It provides examples of finding the greatest common factor and using it to factor polynomials. Key steps involve finding the greatest common monomial factor, dividing each term by the factor, and combining the results into a factored form. Methods like factoring quadratics using FOIL and box multiplication are also reviewed.

GR 8 Math Powerpoint about Polynomial Techniques

-This is a powerpoint inspired by one of Canva displayed presentation.
- This is about Math Polynomials and good for highschoolers presentation for school.
- It consists of 39 pages explaining each of the Polynomial Techniques.
- Good for review or inspired powerpoint.

Factoring polynomials

1. There are several methods for factoring polynomials outlined in the document: factoring using the distributive property, factoring the difference of two squares/cubes, factoring a perfect square trinomial, and factoring general trinomials using trial and error or grouping.
2. Factoring trinomials involves determining the signs in the factors based on the signs of the terms, then finding two factors of the constant term that satisfy the middle term.
3. More complex polynomials can be factored by grouping like terms or using special factoring patterns like the difference of squares/cubes.

March 18, 2015

1. The document outlines the daily lesson plan which includes a warm-up on linear vs quadratic equations, reviewing factoring quadratics and special products like difference of squares.
2. The class will focus on factoring polynomials completely using steps like finding the greatest common factor, looking for special cases like difference of squares, and factoring trinomials.
3. Students are assigned class work from section 3.9 in their notebooks due by Friday which contains multiple factoring problems, including using special products like difference of squares.

March 25, 2014

The document provides an agenda and notes for a math class focusing on factoring polynomials. Tomorrow's lesson will cover factoring trinomials and the difference of squares, while today covers perfect square trinomials, a warm-up on factoring practice, and a review of techniques for factoring completely. It also lists Khan Academy topics and an upcoming factoring test on specific methods.

COT1-PST.pptx

The document provides instructions for factoring perfect square trinomials. It explains that a perfect square trinomial can be factored by taking the square root of the first and last terms. The sign of the middle term is determined by whether the binomial being squared had a positive or negative term. Examples are provided to demonstrate factoring trinomials that are and are not perfect square trinomials. Students are then given practice problems to complete.

Factoring difference of two squares

1. Factoring the difference of two squares involves writing an expression in the form a2 - b2 as the product of the sum and difference of two binomials.
2. To factor an expression using this method, take the square root of the first and last terms and write them as the sum and difference of two binomials that have the same first and last terms.
3. The key characteristics for an expression to be factorable as the difference of two squares are: it has two terms, the first term is a perfect square, it uses subtraction, and the last term is a perfect square.

1PerfSqTri.ppsx

The document discusses factoring perfect square trinomials. A perfect square trinomial is a trinomial that is the result of squaring a binomial. To factor a perfect square trinomial, both the first and last terms must be perfect squares and the middle term must be 2 times the product of the binomial terms with the correct sign. Several examples demonstrate identifying and factoring perfect square trinomials.

1PerfSqTri.ppsx

The document discusses factoring perfect square trinomials. A perfect square trinomial is a trinomial that is the result of squaring a binomial. To factor a perfect square trinomial, both the first and last terms must be perfect squares and the middle term must be 2 times the product of the binomial terms. If these conditions are met, the trinomial can be factored by reversing the process of squaring the binomial. Several examples demonstrate how to determine if a trinomial is a perfect square trinomial and how to factor it if so.

perfect square trinomial

This document provides instruction on perfect square trinomials including defining them, identifying them, factoring them, and working practice problems. It begins by defining a perfect square trinomial as the result of squaring a binomial with the first and last terms being perfect squares and the middle term being twice the product of the square roots of the first and last terms. Examples are provided to illustrate. The document then provides guidance, activities, and an assessment to practice identifying, factoring, and working with perfect square trinomials.

DLLWeek1_3.docx

This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, procedures, and reflections for lessons on factoring polynomials. Specifically, it covers factoring polynomials with common monomial factors, the difference of two squares, the sum and difference of two cubes, perfect square trinomials, and general trinomials. The procedures describe reviewing previous lessons, presenting new material with examples, discussing concepts, practicing skills, developing mastery through activities, and assessing learning. Reflections include the number of students who achieved mastery and require remediation on the topics.

Q1 week 1 (common monomial,sum & diffrence of two cubes,difference of tw...

It consists of ten units in which the first unit focuses on the special products and factors. Its deals with the study of rational algebraic expressions. It aims to empower students with life – long learning and helps them to attain functional literacy. The call of the K to 12 curriculum allow the students to have an active involvement in learning through demonstration of skills, manifestations of communication skills, development of analytical and creative thinking and understanding of mathematical applications and connections.

Factoring Non-Perfect Square Trinomial Lesson Plan

This document contains a lesson plan for teaching factoring non-perfect trinomials in Math 8. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences through various activities, an evaluation, and assignment. Students will learn to define trinomials, factor non-perfect square trinomials, and apply factoring trinomials to geometric figures through guided practice with algebra tiles and examples.

Algebra unit 8.7

This document provides examples and explanations for factoring special cases of polynomials, including perfect square trinomials and the difference of two squares. It includes examples of recognizing, factoring, and explaining if expressions are in one of these forms. One example problem finds the perimeter of a garden given its area as a factored expression and evaluates the perimeter for a given value of x.

Factoring Polynomials in Modular Approach

Factoring Polynomials in Modular Approach

Factoring Strategies

Factoring Strategies

Tema# 2 Repaso de factorización

Tema# 2 Repaso de factorización

March 23, 2015

March 23, 2015

Math Q1 - Week 2.pdf

Math Q1 - Week 2.pdf

Q1-W1-Factoring Polynomials.pptx

Q1-W1-Factoring Polynomials.pptx

Factoring Polynomials with Common Monomial Factor.pptx

Factoring Polynomials with Common Monomial Factor.pptx

GR 8 Math Powerpoint about Polynomial Techniques

GR 8 Math Powerpoint about Polynomial Techniques

Factoring polynomials

Factoring polynomials

March 18, 2015

March 18, 2015

March 25, 2014

March 25, 2014

COT1-PST.pptx

COT1-PST.pptx

Factoring difference of two squares

Factoring difference of two squares

1PerfSqTri.ppsx

1PerfSqTri.ppsx

1PerfSqTri.ppsx

1PerfSqTri.ppsx

perfect square trinomial

perfect square trinomial

DLLWeek1_3.docx

DLLWeek1_3.docx

Q1 week 1 (common monomial,sum & diffrence of two cubes,difference of tw...

Q1 week 1 (common monomial,sum & diffrence of two cubes,difference of tw...

Factoring Non-Perfect Square Trinomial Lesson Plan

Factoring Non-Perfect Square Trinomial Lesson Plan

Algebra unit 8.7

Algebra unit 8.7

elimination

The document discusses using the elimination method to solve systems of linear equations by eliminating one variable, substituting values into the original equations to solve for the remaining variable, and checking that the solutions satisfy both equations. It provides step-by-step examples of using the elimination method to solve two systems of linear equations, eliminating variables by adding or multiplying equations. The document concludes with practice problems for students to solve systems of linear equations using the elimination method.

two intercept form

The document discusses using the two intercept form to find the equation of a line given two points. It provides the two intercept form equation, where a and b are the x and y intercepts. It then works through three examples of finding the line equation using two points and the two intercept form. It lists additional practice problems and their solutions for finding line equations using two points and the two intercept form.

equation of the line using two point form

This document discusses using the two-point form to find the equation of a line given two points. It provides the two-point form equation, examples of using the form to find the slope and y-intercept of lines, and practice problems for determining the equation of lines passing through two points. The goal is to determine the equation in slope-intercept form using the two-point form equation and substituting the x- and y-coordinates of the two points.

point slope form

This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.

common monomial factor

The document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of factoring polynomials by finding the GCF of the numerical coefficients and variable terms. Students are then given practice problems to factor polynomials by finding the GCF and writing the factored form.

1.1 ss factoring the difference of two squares

This document discusses factoring polynomials that are the difference of two squares using the formula a2 - b2 = (a + b)(a - b). It provides examples of factoring polynomials like x2 - 16, 9x2 - 100, and 36m2 - 49n4. It also lists 10 practice problems for factoring polynomials that are differences of two squares and references where readers can learn more.

Revised guidelines on the use of the Special Education Fund

This document provides revised guidelines on the use of the Special Education Fund (SEF) according to Joint Circular No. 1, s. 2017 issued by the Department of Education, Department of Budget and Management, and Department of the Interior and Local Government. It outlines the legal bases, allowable expenses, planning and budgeting process, and monitoring procedures for the allocation and utilization of the SEF. The SEF is a special tax levied locally to provide supplementary funds for the operation, maintenance, and development needs of public schools. The guidelines aim to ensure the SEF is used strategically and efficiently to support priority programs like the K-12 basic education program and early childhood care and development.

elimination

elimination

two intercept form

two intercept form

equation of the line using two point form

equation of the line using two point form

point slope form

point slope form

common monomial factor

common monomial factor

1.1 ss factoring the difference of two squares

1.1 ss factoring the difference of two squares

Revised guidelines on the use of the Special Education Fund

Revised guidelines on the use of the Special Education Fund

Top five deadliest dog breeds in America

Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!

A Strategic Approach: GenAI in Education

Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.

clinical examination of hip joint (1).pdf

described clinical examination all orthopeadic conditions .

Your Skill Boost Masterclass: Strategies for Effective Upskilling

Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan

Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.S1-Introduction-Biopesticides in ICM.pptx

S1-Introduction-Biopesticides in ICM

Assignment_4_ArianaBusciglio Marvel(1).docx

Market Analysis Marvel entertainment.

Natural birth techniques - Mrs.Akanksha Trivedi Rama University

Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.

Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcMain Java[All of the Base Concepts}.docx

This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.

How to Build a Module in Odoo 17 Using the Scaffold Method

Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.

Azure Interview Questions and Answers PDF By ScholarHat

Azure Interview Questions and Answers PDF By ScholarHat

South African Journal of Science: Writing with integrity workshop (2024)

South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa

A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.Advanced Java[Extra Concepts, Not Difficult].docx

This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)

This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3

RPMS Template 2023-2024 by: Irene S. Rueco

Lapbook sobre os Regimes Totalitários.pdf

Lapbook sobre o Totalitarismo.

Pride Month Slides 2024 David Douglas School District

Pride Month Slides DDSD

writing about opinions about Australia the movie

writing about opinions about Australia the movie

বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf

বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...

Top five deadliest dog breeds in America

Top five deadliest dog breeds in America

A Strategic Approach: GenAI in Education

A Strategic Approach: GenAI in Education

clinical examination of hip joint (1).pdf

clinical examination of hip joint (1).pdf

The basics of sentences session 5pptx.pptx

The basics of sentences session 5pptx.pptx

Your Skill Boost Masterclass: Strategies for Effective Upskilling

Your Skill Boost Masterclass: Strategies for Effective Upskilling

S1-Introduction-Biopesticides in ICM.pptx

S1-Introduction-Biopesticides in ICM.pptx

Assignment_4_ArianaBusciglio Marvel(1).docx

Assignment_4_ArianaBusciglio Marvel(1).docx

Natural birth techniques - Mrs.Akanksha Trivedi Rama University

Natural birth techniques - Mrs.Akanksha Trivedi Rama University

Main Java[All of the Base Concepts}.docx

Main Java[All of the Base Concepts}.docx

How to Build a Module in Odoo 17 Using the Scaffold Method

How to Build a Module in Odoo 17 Using the Scaffold Method

Azure Interview Questions and Answers PDF By ScholarHat

Azure Interview Questions and Answers PDF By ScholarHat

South African Journal of Science: Writing with integrity workshop (2024)

South African Journal of Science: Writing with integrity workshop (2024)

Advanced Java[Extra Concepts, Not Difficult].docx

Advanced Java[Extra Concepts, Not Difficult].docx

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...

RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3

RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3

The basics of sentences session 6pptx.pptx

The basics of sentences session 6pptx.pptx

Lapbook sobre os Regimes Totalitários.pdf

Lapbook sobre os Regimes Totalitários.pdf

Pride Month Slides 2024 David Douglas School District

Pride Month Slides 2024 David Douglas School District

writing about opinions about Australia the movie

writing about opinions about Australia the movie

বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf

বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf

- 1. Factors of Polynomials Factoring a Perfect Square Trinomial
- 2. Jessebel G. Bautista Antonio J. Villegas Voc’l High School My Profile
- 3. OBJECTIVES: 1. recall the concept of a perfect square 2. identify a perfect square trinomial 3. use MBM methodology to factor perfect square trinomial
- 4. REVIEW Answer: The square of a number is the number times itself. Question: What is the square of a number?
- 5. REVIEW Answer: 1. The 1st and the last term are perfect square. 2. The middle term is twice the product of the first and the last term. Question: How can you tell if it is a perfect square trinomial?
- 6. This is how Perfect Square Trinomial looks like.
- 7. Activity 1 Find the perfect me! 10x 81 18x X2 4 15x 16x2 -24x 9 10x 28x 4x2 -16x 16 15x 25 49x2 16x2 49 8x 16 24x2 9 25 14x 8x 40x 30x 10x 7x x2 12x 25x2 40 12x2 Description: Look for the different perfect square trinomials found in the box. Answers might be in diagonal, horizontal or vertical in form.
- 8. Answer in Activity 1 Find the perfect me! 10x 81 18x X2 4 15x 16x2 -24x 9 10x 28x 4x2 -16x 16 15x 25 49x2 16x2 49 8x 16 24x2 9 25 14x 8x 40x 30x 10x 7x x2 12x 25x2 40 12x2 Description: Look for the different perfect square trinomials found in the box. Answers might be in diagonal, horizontal or vertical in form.
- 9. Remember: You can use the following relationships to factor perfect square trinomials: Remember to factor out first the greatest common monomial factor before factoring the perfect square trinomial. (First term)2 + 2(First term)(Last term) + (Last term)2 = (First term + Last term)2 (First term)2 – 2(First term)(Last term) + (Last term)2 = (First term – Last term)2
- 10. Illustrative Examples: 1. Factor n2 + 16n + 64 Multi Breaker Map Direction: Factor the following perfect square trinomial using MBM. Get the square root of the first term: Get the square root of the last term: √ n2 = n √64 = 8 Check if the middle term is twice the product of the 1st and last term: 16n = 2(n.8) If the three verifications are satisfied then it’s a PST. Add the factor of the 1st and last term then squared: (n + 8)2
- 11. 2. Factor 4r2 – 12r + 9 Multi Breaker Map Direction: Factor the following perfect square trinomial using MBM. Get the square root of the first term: Get the square root of the last term: √ 4r2 = 2r √9 = 3 Check if the middle term is twice the product of the 1st and last term: 12r = 2(2r . 3) If the three verifications are satisfied then it’s a PST. Subtract the factor of the 1st and last term then squared: (2r - 3)2
- 12. 3. Factor 75t3 + 30t2 + 3t Get the square root of the first term: Get square root of the last term: √25t2 = 5t √1= 1 Check if the middle term is twice the product of the 1st and last term: 10t = 2(5t . 1) If the three verifications are satisfied then it’s a PST. Add the factor of the 1st and last term then squared: (5t + 1)2 Find the common monomial factor to of the trinomial then simplify: (75t3 + 30t2 + 3t)/3t = 25t2 + 10t + 1 Multiply the factor by 3t to equate the trinomial: 3t(5t + 1)2
- 13. Activity 2: To Do…. Group Activity Let’s MBM! Direction: Group the students into 5 groups. Factor any two numbers using MBM. 1. 121c4 + 66c2 + 9 2. 25r2 + 40rn + 16n2 3. 16x2 + 56x + 49 4. 18h2 + 12h + 2 5. 20f 4 – 60f 3 + 45f 2
- 14. Thank you!
- 15. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module https://www.google.com/search?q=perfect+squar e+trinomial&rlz=1C1GCEU_enPH821PH821&sxsrf= ALeKk01FvBiKmtzMSx1P_yasB7YN2q6OGg:158908 9125111&tbm=isch&source=iu&ictx=1&fir=s7xEYX LPsPU05M%253A%252CknBc5lKKuTwkIM%252C_ &vet=1&usg=AI4_- kRLHyz7RChJG0o2UGvenfqB0bW5HA&sa=X&ved= 2ahUKEwj3- sWmyqjpAhXOxIsBHZseAuUQ9QEwFXoECAUQIA#i mgrc=s7xEYXLPsPU05M: