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Warm Up Factor each trinomial. 1. x 2 + 13 x + 40

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

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Warm Up Factor each trinomial. 1. x 2 + 13 x + 40

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  1. 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)

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

  3. Learning Targets Students will be able to: Choose an appropriate method for factoring a polynomial and combine methods for factoring a polynomial.

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

  5. 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

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

  7. 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.

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

  9. Factor 10x2 + 48x + 32 completely. 10x2 + 48x + 32 Factor out the GCF. 2(5x2 + 24x + 16) 2(5x + 4)(x + 4) Factor remaining trinomial.

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

  11. 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

  12. 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. If none of the factoring methods work, the polynomial is said to be unfactorable.

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

  14. 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.

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

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

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

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