Objective Factor polynomials by using the greatest common factor.

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Presentation transcript:

Objective Factor polynomials by using the greatest common factor.

Sometimes the GCF of terms is a binomial 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 3: Factoring Out a Common Binomial Factor Factor each expression. A. 5(x + 2) + 3x(x + 2) The terms have a common binomial factor of (x + 2). 5(x + 2) + 3x(x + 2) (x + 2)(5 + 3x) Factor out (x + 2). B. –2b(b2 + 1)+ (b2 + 1) The terms have a common binomial factor of (b2 + 1). –2b(b2 + 1) + (b2 + 1) –2b(b2 + 1) + 1(b2 + 1) (b2 + 1) = 1(b2 + 1) (b2 + 1)(–2b + 1) Factor out (b2 + 1).

Check It Out! Example 3 Factor each expression. c. 3x(y + 4) – 2y(x + 4) There are no common factors. 3x(y + 4) – 2y(x + 4) The expression cannot be factored. d. 5x(5x – 2) – 2(5x – 2) The terms have a common binomial factor of (5x – 2 ). 5x(5x – 2) – 2(5x – 2) (5x – 2)(5x – 2) (5x – 2)2 (5x – 2)(5x – 2) = (5x – 2)2

Example 4A: Factoring by Grouping Factor each polynomial by grouping. Check your answer. 6h4 – 4h3 + 12h – 8 Group terms that have a common number or variable as a factor. (6h4 – 4h3) + (12h – 8) 2h3(3h – 2) + 4(3h – 2) Factor out the GCF of each group. 2h3(3h – 2) + 4(3h – 2) (3h – 2) is another common factor. (3h – 2)(2h3 + 4) Factor out (3h – 2).

Example 4B: Factoring by Grouping Factor each polynomial by grouping. Check your answer. 5y4 – 15y3 + y2 – 3y (5y4 – 15y3) + (y2 – 3y) Group terms. Factor out the GCF of each group. 5y3(y – 3) + y(y – 3) 5y3(y – 3) + y(y – 3) (y – 3) is a common factor. (y – 3)(5y3 + y) Factor out (y – 3).

Check It Out! Example 4a Factor each polynomial by grouping. Check your answer. 6b3 + 8b2 + 9b + 12 (6b3 + 8b2) + (9b + 12) Group terms. 2b2(3b + 4) + 3(3b + 4) Factor out the GCF of each group. (3b + 4) is a common factor. 2b2(3b + 4) + 3(3b + 4) (3b + 4)(2b2 + 3) Factor out (3b + 4).