Warm Up Factor each trinomial. 1. x2 + 13x + 40 (x + 5)(x + 8) 2. 5x2 – 18x – 8 (5x + 2)(x – 4) 3. Factor the perfect-square trinomial 16x2 + 40x + 25 (4x + 5)(4x + 5) 4. Factor 9x2 – 25y2 using the difference of two squares. (3x + 5y)(3x – 5y)

Add or subtract. G. 2x8 + 7y8 – x8 – y8 2x8 + 7y8 – x8 – y8 x8 + 6y8 H. 9b3c2 + 5b3c2 – 13b3c2 9b3c2 + 5b3c2 – 13b3c2 b3c2

Objectives Choose an appropriate method for factoring a polynomial. Combine methods for factoring a polynomial.

Recall that a polynomial is in its fully factored form when it is written as a product that cannot be factored further.

Tell whether each polynomial is completely factored. If not factor it. A. 3x2(6x – 4) 6x – 4 can be further factored. 6x2(3x – 2) Factor out 2, the GCF of 6x and – 4. completely factored B. (x2 + 1)(x – 5) completely factored

x2 + 4 is a sum of squares, and cannot be factored. Caution

Tell whether the polynomial is completely factored. If not, factor it. A. 5x2(x – 1) completely factored B. (4x + 4)(x + 1) 4x + 4 can be further factored. 4(x + 1)(x + 1) Factor out 4, the GCF of 4x and 4. 4(x + 1)2 is completely factored.

To factor a polynomial completely, you may need to use more than one factoring method. Use the steps below to factor a polynomial completely.

Factor 10x2 + 48x + 32 completely. Factor out the GCF. 2(5x + 4)(x + 4) Factor remaining trinomial.

Factor 8x6y2 – 18x2y2 completely. Factor out the GCF. 4x4 – 9 is a perfect-square binomial of the form a2 – b2. 2x2y2(4x4 – 9) 2x2y2(2x2 – 3)(2x2 + 3)

Factor each polynomial completely. 4x3 + 16x2 + 16x Factor out the GCF. x2 + 4x + 4 is a perfect-square trinomial of the form a2 + 2ab + b2. 4x(x + 2)2

If none of the factoring methods work, the polynomial is said to be unfactorable. For a polynomial of the form ax2 + bx + c, if there are no numbers whose sum is b and whose product is ac, then the polynomial is unfactorable. Helpful Hint

Factor each polynomial completely. 9x2 + 3x – 2 The GCF is 1 and there is no pattern. 9x2 + 3x – 2

Factor each polynomial completely. 12b3 + 48b2 + 48b The GCF is 12b; (b2 + 4b + 4) is a perfect-square trinomial in the form of a2 + 2ab + b2.

Factor each polynomial completely. 4y2 + 12y – 72 Factor out the GCF. 4(y2 + 3y – 18) 4(y – 3)(y + 6) (x4 – x2) x2(x2 – 1) Factor out the GCF. x2(x + 1)(x – 1) x2 – 1 is a difference of two squares.

3q4(3q2 + 10q + 8) Factor each polynomial completely. Factor out the GCF. There is no pattern. 3q4(3q2 + 10q + 8) 9q6 + 30q5 + 24q4

HW pp. 569-571/19-35 odd,40-72 even