Lesson 6 1 Factoring by Greatest Common Factor

Lesson 6. 1 Factoring by Greatest Common Factor Objective: • To factor monomials and polynomials by greatest common factor

Vocabulary Factors that are shared by two or more whole numbers are called common factors. The greatest of these common factors is called the greatest common factor, or GCF. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 32: 1, 2, 4, 8, 16, 32

Example of finding GCF Find the GCF of each pair of numbers. 100 and 60

Example of finding GCF Find the GCF of each pair of monomials. 15 x 3 and 9 x 2

Example of finding GCF Find the GCF of each pair of monomials. 8 x 2 and 7 y 3

Example of finding GCF Helpful Hint If two terms contain the same variable raised to different powers, the GCF will contain that variable raised to the lower power. Find the GCF of each pair of monomials. 18 g 2 and 27 g 3

Example of finding GCF Find the GCF of each pair of monomials. 16 a 6 and 9 b 27 x 2 and 45 x 3 y 2 8 x and 7 v 2

Vocabulary Recall the Distributive Property: ab + ac =a(b + c) The Distributive Property allows you to “factor” out the GCF of the terms in a polynomial to write a factored form of the polynomial.

Vocabulary A polynomial is in its factored form when it is written as a product of monomials and polynomials that cannot be factored further. The polynomial 2(3 x – 4 x) is not fully factored because the terms in the parentheses have a common factor of x.

Example of factoring by GCF Factor each polynomial. Check your answer. 2 x 2 – 4 8 x 3 – 4 x 2 – 16 x

Example of factoring by GCF Factor each polynomial. Check your answer. – 14 x – 12 x 2 5 b + 9 b 3 3 x 3 + 2 x 2 – 10

Example of factoring by GCF Factor each polynomial. Check your answer. – 18 y 3 – 7 y 2 8 x 4 + 4 x 3 – 2 x 2

Vocabulary Sometimes the GCF of terms is a binomial. This GCF is called a common binomial factor. You factor out a common binomial factor the same way you factor out a monomial factor.

Example of factoring by GCF Factor each expression. 5(x + 2) + 3 x(x + 2) – 2 b(b 2 + 1)+ (b 2 + 1) 4 z(z 2 – 7) + 9(2 z 3 + 1)

Example of factoring by GCF Factor each expression. a. 4 s(s + 6) – 5(s + 6) b. 7 x(2 x + 3) + (2 x + 3)

Example of factoring by GCF Factor each expression. c. 3 x(y + 4) – 2 y(x + 4) d. 5 x(5 x – 2) – 2(5 x – 2)

Example of factoring by GCF Factor each polynomial by grouping. Check your answer. 6 h 4 – 4 h 3 + 12 h – 8

Example of factoring by GCF Factor each polynomial by grouping. Check your answer. 5 y 4 – 15 y 3 + y 2 – 3 y

Example of factoring by GCF Factor each polynomial by grouping. Check your answer. 6 b 3 + 8 b 2 + 9 b + 12 4 r 3 + 24 r + r 2 + 6

Example of factoring by GCF Factor each polynomial by grouping. Check your answer. 2 x 3 – 12 x 2 + 18 – 3 x. 15 x 2 – 10 x 3 + 8 x – 12