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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.

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Common monomial factor

This document discusses factoring polynomials by finding the greatest common factor (GCF). It explains that the GCF is a number, variable, or combination that is common to each term. The steps are to find the GCF, divide the polynomial by the GCF, and express the polynomial as a product of the quotient and the GCF. An example showing these steps is provided to factor 6c3d - 12c2d2 + 3cd. Practice problems are included at the end.

Factoring Techniques: Difference of Two Squares

This document contains notes and exercises on factoring the difference of two squares from a Grade 8 mathematics class. It includes examples of factoring various expressions involving differences of two squares. It also provides guidance on determining when an expression can be factored as a difference of two squares and the steps to follow in factoring them. Several practice exercises are provided for students to try factoring differences of two squares on their own.

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.

Factoring Sum and Difference of Two Cubes

This will help you in factoring sum and difference of two cubes.
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Factoring the difference of two squares

The document discusses factoring the difference of two squares through examples such as (x+5)(x-5)=x^2 - 25. It explains that to factor a difference of two squares, we write the expression as the difference of two terms squared, then group the terms with the same bases and opposite signs inside parentheses. Several practice problems are provided to reinforce this technique for factoring completely the difference of two squares.

Factoring with Common Monomial Factor

You will learn how to factor polynomials with common monomial factor.
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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).

Factoring general trinomials

This document provides instructions for factoring trinomials with leading coefficients of 1 or greater than 1. For trinomials with a leading coefficient of 1, the document explains how to list the factors of the last term, identify the factor pair that sums to the middle term, and write the factors. For trinomials with a leading coefficient greater than 1, the instructions are to find the product of the leading and last terms, identify factor pairs that sum to the middle term, rewrite the trinomial, group terms, and factor. Examples are provided to demonstrate the process.

Common monomial factor

This document discusses factoring polynomials by finding the greatest common factor (GCF). It explains that the GCF is a number, variable, or combination that is common to each term. The steps are to find the GCF, divide the polynomial by the GCF, and express the polynomial as a product of the quotient and the GCF. An example showing these steps is provided to factor 6c3d - 12c2d2 + 3cd. Practice problems are included at the end.

Factoring Techniques: Difference of Two Squares

This document contains notes and exercises on factoring the difference of two squares from a Grade 8 mathematics class. It includes examples of factoring various expressions involving differences of two squares. It also provides guidance on determining when an expression can be factored as a difference of two squares and the steps to follow in factoring them. Several practice exercises are provided for students to try factoring differences of two squares on their own.

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.

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 the difference of two squares

The document discusses factoring the difference of two squares through examples such as (x+5)(x-5)=x^2 - 25. It explains that to factor a difference of two squares, we write the expression as the difference of two terms squared, then group the terms with the same bases and opposite signs inside parentheses. Several practice problems are provided to reinforce this technique for factoring completely the difference of two squares.

Factoring with Common Monomial Factor

You will learn how to factor polynomials with common monomial factor.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

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).

Factoring general trinomials

This document provides instructions for factoring trinomials with leading coefficients of 1 or greater than 1. For trinomials with a leading coefficient of 1, the document explains how to list the factors of the last term, identify the factor pair that sums to the middle term, and write the factors. For trinomials with a leading coefficient greater than 1, the instructions are to find the product of the leading and last terms, identify factor pairs that sum to the middle term, rewrite the trinomial, group terms, and factor. Examples are provided to demonstrate the process.

Factoring Polynomials

This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.

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.

Factoring Techniques: Common Monomial Factor

This document contains a mathematics lesson plan on factoring common monomial factors and polynomials. It includes examples of factoring expressions like 4a2b5 and 8a3b4 to find their common monomial factor of 4a2b4. It also teaches finding the greatest common factor of polynomials, like finding the GCF of 6x2y and 9xy is 3xy. Several examples of factoring polynomials are provided, such as factoring 10m - 25n as 5(2m - 5n). Students are given exercises to practice factoring various expressions and polynomials.

Simplifying Rational Algebraic Expressions

If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

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.

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.

Factoring Perfect Square Trinomial

The document discusses perfect square trinomials and how to factor them. It provides examples of factoring various square trinomials using the properties that the first and last terms must be perfect squares, and the middle term must be twice the product of the square roots of the first and last terms. It then has students practice factoring several square trinomial examples on their own.

Division of Radicals.pptx

This document discusses dividing radicals and rationalizing radicals. It provides examples of rationalizing radicals by applying the law of radicals to make the denominator free of radicals. Examples of dividing radicals with the same index are also shown. The steps for dividing radicals are to divide the radicands and rationalize if needed to remove radicals from the denominator. An activity is included where students work in groups to solve radical expressions and present their work.

Graphing polynomial functions (Grade 10)

This document provides instructions on graphing polynomial functions. It discusses identifying the roots, x-intercepts, and y-intercept from the factored form of the polynomial. It shows working through an example of graphing the function y = (x – 2)(x – 1)(x + 3). The key steps are:
1. Identify the roots and y-intercept
2. Arrange the roots in a table
3. Complete the table by calculating y-values for different x-values
4. Plot the points on a graph
5. Sketch the graph

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.

Adding and Subtracting Polynomials - Math 7 Q2W4 LC1

This document discusses adding and subtracting polynomials. It defines key polynomial terms like monomial, binomial, and trinomial. It explains that when adding or subtracting polynomials, only like terms can be combined by adding or subtracting their coefficients while keeping the variable parts the same. Examples are provided to demonstrate adding and subtracting polynomials, including real-life word problems involving combining polynomial expressions to model total areas or profits. The overall goal is for students to learn how to perform operations on polynomials.

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.

Quadratic Equation and discriminant

This document introduces the quadratic formula as a method for solving quadratic equations. It shows the steps for deriving the formula from completing the square and provides examples of its use. The discriminant is defined as b^2 - 4ac from the quadratic formula. The sign of the discriminant determines the number and type of roots: positive discriminant yields two real roots, zero discriminant yields one real root, and negative discriminant yields two complex roots. Examples are provided to illustrate each case.

Square of a binomial

The document discusses how to find the square of a binomial expression using the formula F2 + 2FL + L2, where:
- F is the first term of the binomial
- L is the last term of the binomial
- F2 is the square of the first term
- 2FL is twice the product of the first and last terms
- L2 is the square of the last term
It provides examples of using this formula to find the square of binomial expressions like (x + 2)2, (x - 3)2, (m + 4)2, and (x3 – 2y)2. The key steps are to identify the first and last terms and plug

Rational Expressions

To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.

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.

Common Monomial Factor

This document discusses factoring polynomials by common monomial factor. It defines factoring as the reverse of multiplication and finding the prime factors of an expression. The key technique covered is finding the greatest common monomial factor (GCM), which is the greatest common factor of the coefficients multiplied by the greatest common factor of the variables. Examples are provided to demonstrate factoring out the GCM of expressions like 3x + 3y and 2x^3 - 6x^2. Readers are reminded that factoring is finding the factors and the GCM is the product of the coefficient and variable GCFs.

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 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.

Sum and Difference of 2 cubes

The document discusses the formulas for summing and subtracting cubes. It presents the SOAP rule - Sum Of APs, for expanding and factorizing expressions involving sums and differences of cubes. Some examples are given to demonstrate applying the rule, such as expanding y + 8a and factorizing s - st.

Greatest Common Monimial Factor.pptx

Here are the step-by-step procedures to factor polynomials using the greatest common monomial factor:
1. Find the greatest common factor (GCF) of all the numerical coefficients.
2. Find the greatest common factor (GCF) of all the variables with the least exponents.
3. Multiply the GCF of the numerical coefficients with the GCF of the variables to get the greatest common monomial factor (GCMF).
4. Divide the original polynomial by the GCMF. The quotient is the other factor.

March 19, 2014

1) The document discusses different methods for factoring polynomials, including factoring by GCF and factoring by grouping.
2) Factoring by GCF involves finding the greatest common factor of all terms in the polynomial and writing the polynomial as a product with the GCF factored out.
3) Factoring by grouping involves arranging the terms of a four-term polynomial so the first two terms and last two terms each have a common factor, then factoring these common factors out of the pairs of terms.

Factoring Polynomials

This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.

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.

Factoring Techniques: Common Monomial Factor

This document contains a mathematics lesson plan on factoring common monomial factors and polynomials. It includes examples of factoring expressions like 4a2b5 and 8a3b4 to find their common monomial factor of 4a2b4. It also teaches finding the greatest common factor of polynomials, like finding the GCF of 6x2y and 9xy is 3xy. Several examples of factoring polynomials are provided, such as factoring 10m - 25n as 5(2m - 5n). Students are given exercises to practice factoring various expressions and polynomials.

Simplifying Rational Algebraic Expressions

If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u

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.

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.

Factoring Perfect Square Trinomial

The document discusses perfect square trinomials and how to factor them. It provides examples of factoring various square trinomials using the properties that the first and last terms must be perfect squares, and the middle term must be twice the product of the square roots of the first and last terms. It then has students practice factoring several square trinomial examples on their own.

Division of Radicals.pptx

This document discusses dividing radicals and rationalizing radicals. It provides examples of rationalizing radicals by applying the law of radicals to make the denominator free of radicals. Examples of dividing radicals with the same index are also shown. The steps for dividing radicals are to divide the radicands and rationalize if needed to remove radicals from the denominator. An activity is included where students work in groups to solve radical expressions and present their work.

Graphing polynomial functions (Grade 10)

This document provides instructions on graphing polynomial functions. It discusses identifying the roots, x-intercepts, and y-intercept from the factored form of the polynomial. It shows working through an example of graphing the function y = (x – 2)(x – 1)(x + 3). The key steps are:
1. Identify the roots and y-intercept
2. Arrange the roots in a table
3. Complete the table by calculating y-values for different x-values
4. Plot the points on a graph
5. Sketch the graph

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.

Adding and Subtracting Polynomials - Math 7 Q2W4 LC1

This document discusses adding and subtracting polynomials. It defines key polynomial terms like monomial, binomial, and trinomial. It explains that when adding or subtracting polynomials, only like terms can be combined by adding or subtracting their coefficients while keeping the variable parts the same. Examples are provided to demonstrate adding and subtracting polynomials, including real-life word problems involving combining polynomial expressions to model total areas or profits. The overall goal is for students to learn how to perform operations on polynomials.

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.

Quadratic Equation and discriminant

This document introduces the quadratic formula as a method for solving quadratic equations. It shows the steps for deriving the formula from completing the square and provides examples of its use. The discriminant is defined as b^2 - 4ac from the quadratic formula. The sign of the discriminant determines the number and type of roots: positive discriminant yields two real roots, zero discriminant yields one real root, and negative discriminant yields two complex roots. Examples are provided to illustrate each case.

Square of a binomial

The document discusses how to find the square of a binomial expression using the formula F2 + 2FL + L2, where:
- F is the first term of the binomial
- L is the last term of the binomial
- F2 is the square of the first term
- 2FL is twice the product of the first and last terms
- L2 is the square of the last term
It provides examples of using this formula to find the square of binomial expressions like (x + 2)2, (x - 3)2, (m + 4)2, and (x3 – 2y)2. The key steps are to identify the first and last terms and plug

Rational Expressions

To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.

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.

Common Monomial Factor

This document discusses factoring polynomials by common monomial factor. It defines factoring as the reverse of multiplication and finding the prime factors of an expression. The key technique covered is finding the greatest common monomial factor (GCM), which is the greatest common factor of the coefficients multiplied by the greatest common factor of the variables. Examples are provided to demonstrate factoring out the GCM of expressions like 3x + 3y and 2x^3 - 6x^2. Readers are reminded that factoring is finding the factors and the GCM is the product of the coefficient and variable GCFs.

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 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.

Sum and Difference of 2 cubes

The document discusses the formulas for summing and subtracting cubes. It presents the SOAP rule - Sum Of APs, for expanding and factorizing expressions involving sums and differences of cubes. Some examples are given to demonstrate applying the rule, such as expanding y + 8a and factorizing s - st.

Factoring Polynomials

Factoring Polynomials

Adding and subtracting rational expressions

Adding and subtracting rational expressions

Factoring Techniques: Common Monomial Factor

Factoring Techniques: Common Monomial Factor

Simplifying Rational Algebraic Expressions

Simplifying Rational Algebraic Expressions

Addition and subtraction of rational expression

Addition and subtraction of rational expression

Grade 8 Mathematics Common Monomial Factoring

Grade 8 Mathematics Common Monomial Factoring

Factoring Perfect Square Trinomial

Factoring Perfect Square Trinomial

Division of Radicals.pptx

Division of Radicals.pptx

Graphing polynomial functions (Grade 10)

Graphing polynomial functions (Grade 10)

perfect square trinomial

perfect square trinomial

Adding and Subtracting Polynomials - Math 7 Q2W4 LC1

Adding and Subtracting Polynomials - Math 7 Q2W4 LC1

Factoring Polynomials

Factoring Polynomials

Quadratic Equation and discriminant

Quadratic Equation and discriminant

Square of a binomial

Square of a binomial

Rational Expressions

Rational Expressions

7.8.-SPECIAL-PRODUCTS.ppt

7.8.-SPECIAL-PRODUCTS.ppt

Common Monomial Factor

Common Monomial Factor

Lesson 1: Special Products

Lesson 1: Special Products

Factoring the Difference of Two Squares

Factoring the Difference of Two Squares

Sum and Difference of 2 cubes

Sum and Difference of 2 cubes

Greatest Common Monimial Factor.pptx

Here are the step-by-step procedures to factor polynomials using the greatest common monomial factor:
1. Find the greatest common factor (GCF) of all the numerical coefficients.
2. Find the greatest common factor (GCF) of all the variables with the least exponents.
3. Multiply the GCF of the numerical coefficients with the GCF of the variables to get the greatest common monomial factor (GCMF).
4. Divide the original polynomial by the GCMF. The quotient is the other factor.

March 19, 2014

1) The document discusses different methods for factoring polynomials, including factoring by GCF and factoring by grouping.
2) Factoring by GCF involves finding the greatest common factor of all terms in the polynomial and writing the polynomial as a product with the GCF factored out.
3) Factoring by grouping involves arranging the terms of a four-term polynomial so the first two terms and last two terms each have a common factor, then factoring these common factors out of the pairs of terms.

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.

Lecture 03 factoring polynomials good one

This document provides an overview of Chapter 13 from a developmental mathematics textbook. It covers factoring polynomials, including:
- Finding the greatest common factor of polynomials
- Factoring trinomials of the form x^2 + bx + c and ax^2 + bx + c
- Checking factored results by multiplying the factors
The chapter sections are described and examples are provided for each type of factoring technique.

Math083 day 1 chapter 6 2013 fall

This document provides information about a college algebra course taught by Mr. Bianco in Fall 2013. It covers topics like multiplying polynomials using FOIL, factoring polynomials by finding the greatest common factor and factoring trinomials. Examples are provided to demonstrate how to factor polynomials of different forms like ax^2 + bx + c. Students are reminded to check their factoring work by multiplying the factors.

Mathnasium Presentation (1)

This document provides an outline for teaching various factoring techniques. It begins with definitions of algebraic expressions, polynomials, factors, and factoring. It then covers finding the greatest common factor, factoring by using the GCF, factoring by grouping, factoring differences of squares, factoring perfect square trinomials using the special formula, and solving word problems using factoring. Examples are provided for each technique to demonstrate how to factor different polynomial expressions. Special cases like the sum and difference of cubes are also discussed. The document concludes with an explanation of the quadratic formula.

Factoring Polynomials (1).pptx

The document discusses factoring polynomials and finding the roots of polynomial equations. It defines polynomials and polynomial equations. It then covers several methods for factoring polynomials, including factoring polynomials with a common monomial factor, factoring polynomials that are a difference of squares, factoring trinomials, and factoring polynomials by grouping. It also discusses using the factors to find the solutions or roots of a polynomial equation, which are also known as the zeros of a polynomial function.

March 18, 2014

1) The sum of 2 binomials is 5x^2 - 6x. One binomial is 3x^2 - 2x. The problem is to find the other binomial.
2) The document discusses factoring polynomials by finding the greatest common factor (GCF), grouping, difference of squares, sum/difference of cubes, and special cases.
3) Examples are provided for finding the GCF of numbers, monomials, and factoring polynomials using various methods.

March 17, 2015

Today's class will include a warm-up, factoring polynomials using the greatest common factor (GCF) method and factoring by grouping, and Khan Academy assignments due tonight. Students should show all their work to receive credit for class work involving factoring polynomials using GCF and grouping methods.

Algebra unit 8.8

This document provides examples and instructions for factoring polynomials completely using different factoring methods such as greatest common factor, difference of squares, and grouping. It demonstrates how to determine if a polynomial is already fully factored or if additional factoring is possible. Students are shown step-by-step how to choose the appropriate factoring technique and combine methods as needed to fully factor polynomials that include multiple terms and variables. Practice problems with solutions are included to help students apply the factoring skills.

ch13powerpoint.ppt

The document summarizes Chapter 13 on factoring polynomials. It covers the greatest common factor, factoring trinomials of the forms x^2 + bx + c, ax^2 + bx + c, and x^2 + bx + c by grouping. It also discusses factoring perfect square trinomials, difference of two squares, and solving quadratic equations by factoring. Examples are provided to demonstrate each technique.

factoring polynomials

This document outlines key concepts and examples for factoring polynomials. It covers factoring trinomials of the forms x^2 + bx + c, ax^2 + bx + c, and x^2 + bx + c by grouping. Examples are provided to demonstrate finding the greatest common factor of terms, factoring trinomials by finding two numbers whose product and sum meet the given criteria, and checking factoring results using FOIL multiplication. Sections include the greatest common factor, factoring trinomials of the forms x^2 + bx + c and ax^2 + bx + c.

Factoring by grouping ppt

This document outlines key concepts and examples for factoring polynomials. It discusses factoring trinomials of the forms x^2 + bx + c, ax^2 + bx + c, and x^2 + bx + c by grouping. Examples are provided to demonstrate finding the greatest common factor of terms, factoring trinomials by finding two numbers whose product and sum meet the given criteria, and checking factoring results using FOIL. Sections cover the greatest common factor, factoring trinomials of different forms, and solving quadratic equations by factoring.

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The document discusses factoring polynomials. It begins by outlining Swartz's steps for factoring: 1) factor out the greatest common factor (GCF), 2) factor based on the number of terms using techniques like difference of squares or grouping. It then explains how to find the GCF of integers or terms. Several examples are provided of factoring polynomials by finding the GCF and using techniques like difference of squares, grouping, or recognizing perfect square trinomials. Factoring trinomials of the form x^2 + bx + c is also demonstrated.

0.3 Factoring Polynomials

This document provides an overview of various techniques for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF);
2) Factoring by grouping terms with a common factor;
3) Factoring perfect square trinomials where the first and last terms are perfect squares;
4) Factoring trinomials using techniques like the reverse box method or grouping.

Factoring GCF difference of squares.ppt

This document discusses different factoring methods including the greatest common factor method and difference of two squares method. It provides examples of factoring polynomials using each method and emphasizes that the greatest common factor method should always be tried first before other factoring techniques. Students are given practice problems to factor polynomials using these methods and are reminded that sometimes a combination of factoring approaches is needed.

Factoring GCF and Grouping

- The document discusses factoring expressions using the greatest common factor (GCF) method and grouping method.
- With the GCF method, the greatest common factor is determined for each term and factored out.
- The grouping method is used when there are 4 or more terms. The first two terms are factored and the second two terms are factored, then the common factor is extracted.
- Examples of applying both methods to factor polynomials are provided and worked through step-by-step.

March 26

This document provides steps and examples for factoring trinomials of the form ax^2 + bx + c. It begins with reviewing special cases like difference of squares and perfect square trinomials. It then outlines a 6-step process for factoring general trinomials: 1) multiply the leading coefficient and constant, 2) find factors of their product that sum to the middle term, 3) rewrite replacing the middle term, 4) factor by grouping, 5) factor out common binomials, 6) check for complete factorization. Examples are provided applying these steps to fully factor trinomials.

(7) Lesson 5.8 - Factor Linear Expressions

1. The document provides examples of factoring linear expressions using the greatest common factor (GCF) method. It shows how to write expressions as products of their GCF and remaining factors using prime factorizations and algebra tiles.
2. One example factors the expression 15x + 18 as 3(5x + 6), where 3 is the GCF of 15x and 18. This represents possible dimensions of a garden with area (15x + 18) square feet.
3. Numbers and symbols can represent mathematical ideas by factoring linear expressions. This allows expressions to model real-world situations involving quantities and their relationships.

Polynomials with common monomial factors.pptx

This document contains a lesson on factoring polynomials. It begins with examples of factoring various polynomials and identifying the greatest common factor. It then discusses key terminology related to factoring like common monomial factor and factor. The document provides step-by-step worked examples of factoring polynomials. It concludes with a generalization section and seat work problems for students to practice factoring polynomials.

Greatest Common Monimial Factor.pptx

Greatest Common Monimial Factor.pptx

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Lecture 03 factoring polynomials good one

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ch13powerpoint.ppt

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factoring polynomials

factoring polynomials

Factoring by grouping ppt

Factoring by grouping ppt

Swartz Factoring

Swartz Factoring

0.3 Factoring Polynomials

0.3 Factoring Polynomials

Factoring GCF difference of squares.ppt

Factoring GCF difference of squares.ppt

Factoring GCF and Grouping

Factoring GCF and Grouping

March 26

March 26

(7) Lesson 5.8 - Factor Linear Expressions

(7) Lesson 5.8 - Factor Linear Expressions

Polynomials with common monomial factors.pptx

Polynomials with common monomial factors.pptx

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.

factoring perfect square trinomial

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.

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.

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.

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

factoring perfect square trinomial

factoring perfect square trinomial

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

writing linear equation

writing linear equation

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

Thesis Statement for students diagnonsed withADHD.ppt

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- 1. Factors of Polynomials COMMON MONOMIAL FACTOR
- 2. Jessebel G. Bautista Antonio J. Villegas Voc’l High School My Profile
- 3. Objectives: –recall GCF –factor polynomials whose terms have common monomial factor –think deductively using ECM –relate factoring in real life
- 4. Drill: Give the greatest common factor (CGF) of the following expressions. 1. 12, 15, 18 2. 24, 36, 72 3. x3, x2, x 4. x2y2, xy4, x2y2 5. 5a3, 10a2, 15a 6. 30b4, 45b2, 60b3 7. 24x2y2, 40x2y3, 48xy4 8. 100m6n8,125m3n5, 250mn 9. (x -2y)4, (x - 2y)2, (x - 2y) 10. 12(a + b)5, 36(a + b)3, 48(a + b)
- 5. Activity 1 FINDING COMMON Description: Your task in this activity is to identify common things that are present in the three pictures. Questions: 1. What are the things common to these pictures? 2. Are there things that make them different? 3. Can you spot things that are found on one picture but not on the other two? 4. What are the things common to two pictures but not on the other?
- 6. The activity in the previous slides gave us the idea about the Greatest Common Monomial Factor. Now, on the next slide. Study the example of the ECM on how factoring the Greatest Common Monomial Factor is being done.
- 7. Example – Conclusion Map (ECM) Direction: Let the students write the conclusion and their example given the ECM. Polynomial 6m + 8 GCF 2 Quotient of Polynomial 3m + 4 Factored Form 2 (3m +4) Polynomial 15x2+10 xy GCF 5x Quotient of polynomial 3x + 2y Factored Form 5x (3x +2y) Polynomial 5t4 + 4t3 + t2 GCF t2 Quotient of polynomial 5t2 + 4t + 1 Factored Form t2 (5t2 +4t + 1) Example 1 Example 2 Example 3 Conclusion Your own example
- 8. Examples
- 9. 1. Factor : 12x3y5 – 20x5y2z Steps 1: Find the greatest common factor of the numerical coefficients. The GCF of 12 and 20 is 4.
- 10. 1. Factor : 12x3y5 – 20x5y2z Steps 2: Find the variable with the least exponent that appears in each term of the polynomial. x and y are both common to all terms and 3 is the smallest exponent for x and 2 is the smallest exponent of y, thus, x3y2 is the GCF of the variables.
- 11. 1. Factor : 12x3y5 – 20x5y2z Steps 3: The product of the greatest common factor in steps (1) and (2) is the GCF of the polynomial. 4x3y2 is the GCF of 12x3y5 – 20x5y2z.
- 12. 1. Factor : 12x3y5 – 20x5y2z Steps 4: To completely factor the given polynomial, divide the polynomial by its GCF, the resulting quotient is the other factor. The factored form of 12x3y5 – 20x5y2z is 4x3y2(3y3 – 5x2z)
- 13. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 1: Find the greatest common factor of the numerical coefficients. Factor: 12 = 3.4 16 = 4.4 28 = 7.4 The GCF of 12, 16 and 28 is 4.
- 14. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 2: Find the variable with the least exponent that appears in each term of the polynomial. x is common to all terms and 3 is the smallest exponent for x . thus, x3 is the GCF of the variables.
- 15. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 3: The product of the greatest common factor in steps (1) and (2) is the GCF of the polynomial. 4x3 is the GCF of 12x5y4 – 16x3y4 + 28x6
- 16. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 4: To completely factor the given polynomial, divide the polynomial by its GCF, the resulting quotient is the other factor. The factored form of 12x5y4 – 16x3y4 + 28x6 is 4x3(3x2y4 – 4y4 +7x3)
- 17. Direction: Factor the following. 1. 15x2y + 20xy2 2. 14x4y2 – 21x3y5 3. 32a6b6 + 72a7b5 4. -30m4n3 + 40m5n4 5. 90x5y5 – 99x6y6 6. 30a7b8 – 18a8b6 – 6a7b7 7. -36p3q4 + 60p2q3 – 84p3q5 8. 4y3 – 20y2 + 24y 9. 16p2r5 + 48p3r6 – 24p4 10. 45a6b3 – 60a4b2 + 75a3b4 ACTIVITY 3: To Do…
- 19. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module