8th Alg - L7.4--Feb9
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The document contains examples and explanations of concepts related to polynomials, including: - Definitions of monomial, binomial, trinomial, and polynomial based on the number of terms. - The degree of a monomial is the sum of its variable exponents, and the degree of a polynomial is the greatest degree of any term. - Polynomials can be written in standard form with terms in descending degree order. - Examples are provided of identifying polynomials, finding degrees, and writing polynomials in standard form.
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7.6 notes b
1) The document defines polynomials as expressions that can be written as the sum of one or more monomials. A monomial is the product of a number, variable, and nonnegative integer powers.
2) The degree of a monomial is the sum of the exponents of its variables. The degree of a polynomial is the highest degree among its monomial terms.
3) Polynomials are classified by degree, with linear having degree 1, quadratic degree 2, cubic degree 3, and so on. Basic arithmetic with polynomials involves combining like terms.
Polynomials Introduction
1. The student will learn about finding the degree of a polynomial, arranging polynomial terms in ascending or descending order, and identifying whether an expression is a polynomial.
2. Key terms include: monomial, polynomial, degree of a monomial or polynomial, ascending order, descending order, and leading coefficient.
3. Examples are provided for finding the degree of monomials and polynomials, arranging polynomial terms in ascending and descending order, and identifying the leading coefficient of a polynomial.
7th Math (C2) - L46--Jan27
1) This document is an assignment that includes a warm-up with 5 math problems and a lesson on rates and unit prices with examples to solve.
2) The warm-up includes solving a fraction, finding the mode of a data set, calculating the mean of the first 5 prime numbers, dividing a decimal and writing a fraction as a decimal.
3) The lesson defines rates as a ratio of two measures and unit price as the cost of a single product unit. It presents the distance-rate-time formula and includes examples to practice calculating rates and unit prices.
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.
Factoring with Common Monomial Factor
You will learn how to factor polynomials with common monomial factor.
For more instructional resources, CLICK me here! 👇👇👇
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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.
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.
Algebra 7 Point 2
This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of factoring polynomials by taking out the GCF of 5y2 + 10y + 20, t5 + 8t4 + t3, and 2b4 - 10b3 + 8b2. It also discusses using the distributive property to factor polynomials like 3x2 - 9x + 6.
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7.6 notes b
1) The document defines polynomials as expressions that can be written as the sum of one or more monomials. A monomial is the product of a number, variable, and nonnegative integer powers.
2) The degree of a monomial is the sum of the exponents of its variables. The degree of a polynomial is the highest degree among its monomial terms.
3) Polynomials are classified by degree, with linear having degree 1, quadratic degree 2, cubic degree 3, and so on. Basic arithmetic with polynomials involves combining like terms.
Polynomials Introduction
1. The student will learn about finding the degree of a polynomial, arranging polynomial terms in ascending or descending order, and identifying whether an expression is a polynomial.
2. Key terms include: monomial, polynomial, degree of a monomial or polynomial, ascending order, descending order, and leading coefficient.
3. Examples are provided for finding the degree of monomials and polynomials, arranging polynomial terms in ascending and descending order, and identifying the leading coefficient of a polynomial.
7th Math (C2) - L46--Jan27
1) This document is an assignment that includes a warm-up with 5 math problems and a lesson on rates and unit prices with examples to solve.
2) The warm-up includes solving a fraction, finding the mode of a data set, calculating the mean of the first 5 prime numbers, dividing a decimal and writing a fraction as a decimal.
3) The lesson defines rates as a ratio of two measures and unit price as the cost of a single product unit. It presents the distance-rate-time formula and includes examples to practice calculating rates and unit prices.
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.
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
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.
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.
Algebra 7 Point 2
This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of factoring polynomials by taking out the GCF of 5y2 + 10y + 20, t5 + 8t4 + t3, and 2b4 - 10b3 + 8b2. It also discusses using the distributive property to factor polynomials like 3x2 - 9x + 6.
Factoring Polynomials with common monomial factor
This document discusses common monomial factoring, which is writing a polynomial as a product of two polynomials where one is a monomial that factors each term. It provides examples of finding the greatest common factor (GCF) of terms in a polynomial and using it to factor the polynomial. Specifically, it factors polynomials like 4m^2 + 10m^4, 6x^4 + 9x^2y + 15x^5y, and 25b^3c^2 - 5b^2c.
Factoring the greatest common monomial factor
This document discusses factoring polynomials by finding the greatest common factor (GCF). It explains that factoring a polynomial is the reverse of multiplying a monomial and polynomial. Examples are provided of factoring polynomials by identifying the GCF and rewriting the polynomial as a product of the GCF and other factors. The process of factoring out the GCF is demonstrated step-by-step for several examples.
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Are you scared of that algebraic sums? Just view this presentation an you can learn about each and every algebraic identities. Just view this and Now take full marks in your tests..
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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.
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This document provides an overview of polynomials, including:
1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
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.
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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
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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.
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- Examples of expressions such as x + 3, 2y - 5, and 4xy + 7 which are formed from variables and constants.
- The value of an expression changes depending on the values chosen for its variables.
- Expressions can be made up of one or more terms which are the products of factors.
- Monomials contain one term, binomials contain two terms, and trinomials contain three terms. Polynomials can contain any number of terms.
- Additions, subtractions, and multiplications of algebraic expressions are demonstrated.
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The document provides a summary of factoring methods:
- Reviewing factoring methods covered such as greatest common factor (GCF) and factoring trinomials
- Announcing that test grades have been posted for one class and quarter grades will be posted for another class tomorrow
- Introducing a new factoring method called "difference of squares" and new Khan Academy topics being added
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Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.
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.
(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.
9.4
Dividing polynomials involves writing the division as a fraction and using properties of exponents. Terms are divided using the quotient of powers property. Any remaining terms are the remainder. Examples show dividing monomials, polynomials by monomials and binomials, checking work, and rewriting polynomials with missing terms or nonzero remainders.
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Hiral polynomials mini
- This document defines key terms related to polynomials such as mono, bi, tri, and poly prefixes and defines a polynomial as a mathematical expression with one or more terms where the variable index is a whole number.
- Polynomials are classified as monomials (one term), binomials (two terms), or trinomials (three terms). Degrees of polynomials and monomials are defined as the sum of the exponents of the variables.
- Examples are provided to demonstrate identifying polynomials and classifying them by type, as well as finding the degree of monomials and polynomials.
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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.
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Prashant tiwari ppt.on
The document discusses polynomials and their properties. It begins by defining a polynomial as an expression with terms that are products of numbers and variables with exponents, where the terms are added or subtracted. It then discusses how to classify polynomials based on their degree or number of terms. The document also covers how to perform operations such as addition, subtraction, and multiplication on polynomials by using properties like the distributive property.
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This document provides an overview of polynomials, including:
1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
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The document defines rational expressions as expressions that can be written as a ratio of two polynomials where the denominator is not 0. It provides examples of finding excluded values, which make the expression undefined, by setting the denominator equal to 0. It also discusses simplifying rational expressions by dividing out common factors in the numerator and denominator and putting them in simplest form. Examples are provided of factoring, dividing out monomials, recognizing opposites, and simplifying a rational model.
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- 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
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.
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The document provides information about algebraic expressions including:
- Examples of expressions such as x + 3, 2y - 5, and 4xy + 7 which are formed from variables and constants.
- The value of an expression changes depending on the values chosen for its variables.
- Expressions can be made up of one or more terms which are the products of factors.
- Monomials contain one term, binomials contain two terms, and trinomials contain three terms. Polynomials can contain any number of terms.
- Additions, subtractions, and multiplications of algebraic expressions are demonstrated.
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The document provides a summary of factoring methods:
- Reviewing factoring methods covered such as greatest common factor (GCF) and factoring trinomials
- Announcing that test grades have been posted for one class and quarter grades will be posted for another class tomorrow
- Introducing a new factoring method called "difference of squares" and new Khan Academy topics being added
Adding and subtracting polynomials
Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.
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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.
(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.
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Dividing polynomials involves writing the division as a fraction and using properties of exponents. Terms are divided using the quotient of powers property. Any remaining terms are the remainder. Examples show dividing monomials, polynomials by monomials and binomials, checking work, and rewriting polynomials with missing terms or nonzero remainders.
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The document discusses polynomials and factoring polynomials. It defines polynomials as expressions with terms added or subtracted, where terms are products of numbers and variables with exponents. It provides examples of monomials, binomials, trinomials, and polynomials based on the number of terms. It also discusses finding the greatest common factor of a polynomial to factor out a monomial.
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- This document defines key terms related to polynomials such as mono, bi, tri, and poly prefixes and defines a polynomial as a mathematical expression with one or more terms where the variable index is a whole number.
- Polynomials are classified as monomials (one term), binomials (two terms), or trinomials (three terms). Degrees of polynomials and monomials are defined as the sum of the exponents of the variables.
- Examples are provided to demonstrate identifying polynomials and classifying them by type, as well as finding the degree of monomials and polynomials.
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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.
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The document defines and provides examples of various algebraic expressions including monomials, binomials, trinomials, and polynomials. It explains that a polynomial is an algebraic expression with variables that have only non-negative integral powers. The degree of a polynomial refers to the highest power of the variable. Quadratic polynomials specifically are polynomials of degree 2. The document also discusses finding zeros of polynomials and provides examples of factoring polynomials using common identities.
February 8
The document provides a review of exponents and scientific notation in preparation for a math test on Monday. It includes examples of operations with exponents, expressions to convert between scientific and standard notation, and an introduction to polynomials. Students are reminded to complete Khan Academy topics by 7:00 pm Saturday to best prepare for the upcoming test.
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The document outlines tasks for the day which include collecting signed tests and providing work time for students. It also lists 4 assignments - an algebra final review covering chapters 10-11 and 7-8-9 due the next day, checking if a chapter 11 test was signed for extra credit, and noting the final exam is on Thursday.
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The document outlines tasks to complete for the work day including collecting signed tests, working on million dollar projects, checking if a timed test was done, and preparing for VBS balls. It also lists assignments for students to get test #12 signed for extra credit and take the final exam, test #13, on Thursday.
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The document outlines tasks for the day which include returning graded work, doing frog origami if there is time, and assignments. Students need to get Test #12 signed for extra credit, Test #13 will be on Tuesday, and the Frog Olympics activity will take place on Thursday.
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The document outlines tasks and assignments for a work day, including returning graded work, doing a mental math timing activity, and having work time. It also lists three assignments: a million dollar activity due Monday, the option to get a test signed for extra credit, and a final exam scheduled for Thursday.
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- 1. Lesson 7.4 WarmUp: Simplify each expression. 1) (5x2y)(3x4) 2) (xy)3(xz)4 3) (3pr2)5 4) r7n7t2 n3r3t2 5) (2mn2)3 4m6n4 1
- 4. Lesson 7.4 examples: Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial. A) 5xy + 7yz yes binomial B) 15 yes monomial C) 7x3 9b no... D) 6a3 + 4b + b + 10 yes trinomial 4
- 5. Find the degree of each polynomial. E) 3r4 4 F) b + 6 1 G) 8x5y4 2x8 9 H) 12 0 5
- 6. Write each polynomial in standard form. Identify the leading coefficient. I) 3x + 1 + 2x2 2x2 + 3x + 1 ; 2 J) 25 x3 + x x3 + x + 25 ; 1 K) 6x3 7x5 + x 2x2 + 1 7x5 + 6x3 2x2 + x + 1 ; 7 6