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