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8-6 Choosing a Factoring Method 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) Holt Algebra 1 8-6 Choosing a Factoring Method Add or subtract. G. 2x8 + 7y8 – x8 – y8 2x8 + 7y8 – x8 – y8 x8 + 6y8 H. 9b3c2 + 5b3c2 – 13b3c2 9b3c2 + 5b3c2 – 13b3c2 b3c2 Holt Algebra 1 8-6 Choosing a Factoring Method Learning Targets Students will be able to: Choose an appropriate method for factoring a polynomial and combine methods for factoring a polynomial. Holt Algebra 1 8-6 Choosing a Factoring Method Recall that a polynomial is in its fully factored form when it is written as a product that cannot be factored further. Holt Algebra 1 8-6 Choosing a Factoring Method 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 Holt Algebra 1 8-6 Choosing a Factoring Method Caution x2 + 4 is a sum of squares, and cannot be factored. Holt Algebra 1 8-6 Choosing a Factoring Method Tell whether the polynomial is completely factored. If not, factor it. A. 5x2(x – 1) completely factored B. (4x + 4)(x + 1) 4(x + 1)(x + 1) 4x + 4 can be further factored. Factor out 4, the GCF of 4x and 4. 4(x + 1)2 is completely factored. Holt Algebra 1 8-6 Choosing a Factoring Method To factor a polynomial completely, you may need to use more than one factoring method. Use the steps below to factor a polynomial completely. Holt Algebra 1 8-6 Choosing a Factoring Method Factor 10x2 + 48x + 32 completely. 10x2 + 48x + 32 2(5x2 + 24x + 16) Factor out the GCF. 2(5x + 4)(x + 4) Factor remaining trinomial. 4 20x 16 x 5x 2 4x 5x Holt Algebra 1 4 80x 2 20x 4x 24x 8-6 Choosing a Factoring Method Factor 8x6y2 – 18x2y2 completely. 8x6y2 – 18x2y2 2x2y2(4x4 – 9) 2x2y2(2x2 – 3)(2x2 + 3) Holt Algebra 1 Factor out the GCF. 4x4 – 9 is a perfect-square binomial of the form a2 – b2. 8-6 Choosing a Factoring Method Factor each polynomial completely. 4x3 + 16x2 + 16x 4 x x2 4 x 4 4x x 2 x 2 4x(x + 2)2 Holt Algebra 1 Factor out the GCF. x2 + 4x + 4 is a perfect-square trinomial of the form a2 + 2ab + b2. 8-6 Choosing a Factoring Method If none of the factoring methods work, the polynomial is said to be unfactorable. Helpful Hint 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. Holt Algebra 1 8-6 Choosing a Factoring Method Factor each polynomial completely. 9x2 + 3x – 2 2 6x 2 3x 9x 2 3x 3x 1 9x2 + 3x – 2 Holt Algebra 1 The GCF is 1 and there is no pattern. 18x 2 6x 3x 3x 3x 13x 2 8-6 Choosing a Factoring Method Factor each polynomial completely. 12b3 + 48b2 + 48b The GCF is 12b; (b2 + 4b + 4) is a perfect-square 2 12b b 4b 4 trinomial in the form of 2 + 2ab + b2. a 12b b 2 b 2 12b b 2 Holt Algebra 1 2 8-6 Choosing a Factoring Method 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. Holt Algebra 1 8-6 Choosing a Factoring Method Factor each polynomial completely. 9q6 + 30q5 + 24q4 3q4(3q2 + 10q + 8) Factor out the GCF. There is no pattern. 2 2 6q 8 q 3q 2 4q 24q 6q 4q 10q 3q 4 9q6 + Holt Algebra 1 30q5 + 24q4 3q 3q 4 q 2 4 8-6 Choosing a Factoring Method HW pp. 569-571/19-35 odd,40-72 even Holt Algebra 1