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Unit 9 – Factoring Polynomials

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1 Unit 9 – Factoring Polynomials
Topic: Greatest Common Factors

2 Vocabulary Factor Common factors Greatest Common Factor (GCF)
Whole number divisors of another whole number. Ex. 3 is a factor of 27 Variable divisors of another variable. Ex. x2 is a factor of x5 Common factors Factors shared by two or more monomials. Ex. 3 is a common factor of 9 and 27 Greatest Common Factor (GCF) Largest common factor of two or more monomials. Ex. 9 is the GCF of 9 & 27

3 Prime Factorization Prime number factors of a whole number.
Prime factors can be found using a factor tree. Prime number

4 Finding GCF of numbers – Listing factors
List factors of each number and identify the GCF. Example: Find the GCF of 18 and 27. Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 27: 1, 3, 9, 27 GCF = 9

5 Finding GCF of numbers – Using Factor Trees
Find the prime factors of each number. The GCF will be the product of common primes. Example: Find the GCF of 18 and 27. Prime factorization of 18: 2 x 3 x 3 Prime factorization of 27: 3 x 3 x 3 Common primes: 3 x 3 GCF = 9

6 Finding GCF of variables
GCF will include a common variable base & the lowest exponent of given terms. Example: Find the GCF of x3, x5y, & x4y2 Common variable base: x (1st term doesn’t have a y in it) Lowest exponent of x: 3 GCF of x3, x5y, & x4y2= x3

7 Finding GCF of monomials
Must find GCF of coefficients AND variable(s). Example: Find the GCF of 3x3 and 6x2 GCF of 3 & 6: 3 GCF of x3 and x2: x2 GCF of 3x3 & 6x2= 3x2

8 Factoring polynomials by GCF
Rewriting polynomials as products of monomials & polynomials that cannot be factored further. Find GCF of the given terms, then factor (divide) it out. Example: Factor the polynomial GCF = 5y; divide each term by 5y to find remainders. NOTE: GCF MUST appear in final answer (Think of factoring as “un-distributing”).

9 Factoring out a common binomial
Two monomials that are multiplied by the same binomial. The binomial can be factored out, leaving the two monomials together to form another binomial. Example: Factor (x – 2) factors out, leaving 4x & 5 to form a binomial.

10 Factoring by grouping Grouping terms of a polynomial by similar GCFs to find a common binomial. Example: Factor Rewrite the polynomial in standard form, then group the first 2 terms & the last 2 terms. Factor a GCF out of each group (this should give you a common binomial). Factor out the common binomial.

11 Journal Entry Title: GCF 3-2-1
Identify 3 things you already knew from the material in the PowerPoint. Identify 2 new things you learned. Identify 1 question you still have.

12 Homework Textbook Section 8-1 (p. 527): 16-30 even
Textbook Section 8-2 (p. 535): even, even DUE 3/16

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