1 / 19

Choose an appropriate method for factoring a polynomial.

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.

kitra-jordan
Download Presentation

Choose an appropriate method for factoring a polynomial.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

  3. Example 1: Determining Whether a Polynomial is Completely Factored Tell whether each expression is completely factored. If not, factor it. A. 3x2(6x– 4) 3x2(6x–4) 6x – 4 can be further factored. 6x2(3x– 2) Factor out 2, the GCF of 6x and – 4. 6x2(3x– 2) is completely factored. B. (x2 + 1)(x– 5) (x2 + 1)(x– 5) Neither x2 +1 nor x – 5 can be factored further. (x2 + 1)(x– 5) is completely factored.

  4. Check It Out! Example 1 Tell whether the polynomial is completely factored. If not, factor it. A. 5x2(x– 1) Neither 5x2 nor x – 1 can be factored further. 5x2(x– 1) 5x2(x– 1) is completely factored. B. (4x + 4)(x + 1) (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.

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

  6. Example 2A: Factoring by GCF and Recognizing Patterns Factor 10x2 + 48x + 32 completely. Check your answer. 10x2 + 48x + 32 Factor out the GCF. 2(5x2 + 24x + 16) 2(5x + 4)(x + 4) Factor remaining trinomial.

  7. Example 2B: Factoring by GCF and Recognizing Patterns Factor 8x6y2– 18x2y2 completely. Check your answer. 8x6y2– 18x2y2 Factor out the GCF. 4x4 – 9is a perfect-square trinomial of the form a2 – b2. 2x2y2(4x4– 9) 2x2y2(2x2– 3)(2x2 + 3) a = 2x, b = 3

  8. 4x3 + 16x2 + 16x 4x(x2 + 4x + 4) Check It Out! Example 2a Factor each polynomial completely. Check your answer. 4x3 + 16x2 + 16x 4x(x + 2)2

  9. Check It Out! Example 2b Factor each polynomial completely. Check your answer. 2x2y– 2y3 2x2y– 2y3 2y(x2–y2) 2y(x + y)(x–y)

  10. ( x + )( x + ) Factors of 9 Factors of –2Outer+Inner  1 and –2 1(–2) + 9(1) = 7 1 and 9  1 and –2 3(–2) + 3(1) = –3 3 and 3  –1 and 2 3(2) + 3(–1) = 3 3 and 3 (3x– 1)(3x + 2) Example 3A: Factoring by Multiple Methods Factor each polynomial completely. 9x2 + 3x– 2 The GCF is 1 and there is no pattern. 9x2 + 3x– 2 a = 9 and c = –2; Outer + Inner = 3

  11. (b + )(b + ) Factors of 4Sum  1 and 4 5  2 and 2 4 Example 3B: Factoring by Multiple Methods Factor each polynomial completely. 12b3 + 48b2 + 48b 12b(b2 + 4b + 4) 12b(b + 2)(b + 2) 12b(b + 2)2

  12. (y + )(y + ) Factors of –18Sum  –1 and 18 17  –2 and 9 7  –3 and 6 3 Example 3C: Factoring by Multiple Methods Factor each polynomial completely. 4y2 + 12y– 72 4(y2 + 3y– 18) 4(y –3)(y + 6)

  13. Example 3D: Factoring by Multiple Methods. Factor each polynomial completely. (x4–x2) Factor out the GCF. x2(x2– 1) x2 – 1is a difference of two squares. x2(x + 1)(x– 1)

  14. ( x + )( x + ) Factors of 3 Factors of 4Outer+Inner  1 and 4 3(4) + 1(1) = 13 3 and 1  2 and 2 3(2) + 1(2) = 8 3 and 1  4 and 1 3(1) + 1(4) = 7 3 and 1 (3x + 4)(x + 1) Check It Out! Example 3a Factor each polynomial completely. 3x2 + 7x + 4 3x2 + 7x + 4

  15. (p + )(p + ) Factors of – 6 Sum  – 1 and 6 5 Check It Out! Example 3b Factor each polynomial completely. 2p5 + 10p4– 12p3 2p3(p2 + 5p– 6) 2p3(p + 6)(p– 1)

  16. ( q + )( q + ) Factors of 3 Factors of 8Outer+Inner  1 and 8 3(8) + 1(1) = 25 3 and 1  2 and 4 3(4) + 1(2) = 14 3 and 1  4 and 2 3(2) + 1(4) = 10 3 and 1 3q4(3q + 4)(q + 2) Check It Out! Example 3c Factor each polynomial completely. 9q6 + 30q5 + 24q4 3q4(3q2 + 10q + 8)

  17. Check It Out! Example 3d Factor each polynomial completely. 2x4 + 18 2(x4 + 9) Factor out the GFC. x4 + 9 is the sum of squares and that is not factorable. 2(x4 + 9) is completely factored.

  18. Lesson Quiz Tell whether the polynomial is completely factored. If not, factor it. 1. (x + 3)(5x + 10) 2. 3x2(x2 + 9) no; 5(x+ 3)(x + 2) completely factored Factor each polynomial completely. Check your answer. 3.x3 + 4x2 + 3x + 12 4. 4x2 + 16x – 48 4(x + 6)(x– 2) (x + 4)(x2 + 3) 5. 18x2– 3x– 3 6. 18x2– 50y2 3(3x + 1)(2x– 1) 2(3x + 5y)(3x– 5y) 7. 5x –20x3 + 7 – 28x2 (1 + 2x)(1 – 2x)(5x + 7)

More Related