1 / 16

Mastering Polynomial Factoring Techniques

Learn to factor polynomials using common factors and binomial factors. Practice finding factors of polynomials and factor by grouping with clear examples. Enhance your skills in polynomial factorization.

marny-cook
Télécharger la présentation

Mastering Polynomial Factoring Techniques

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. 9.5 Common Factors Objectives • Factor a polynomial by using the greatest common factor. • Factor a polynomial by using a binomial factor. Glossary Terms common binomial factor factor Greatest Common Factor

  2. 9.5 Common Factors Factor using the GCF 6ab – 3a = 3a(2b – 1) 5am – 5an = 5a(m – n) 14a2 – 4a = 2a(7a – 2) 4y – 16y2 = 4y(1 – 4y) 5x2yz + 10y2z = 5yz(x2 + 2y)

  3. 9.5 Common Factors Factor using the GCF (20x4 – 12x3 + 8x2) ÷ (4x2) 20x4 – 12x3 + 8x2 20x4 – 12x3 + 8x2 = 4x2 4x2 4x2 4x2 = 4x2(5x2 – 3x + 2)  = 20x4 – 12x3 + 8x2

  4. 9.5 Common Factors Factor using the GCF (24x4 – 12x2 + 18x) ÷ (6x) 24x4 – 12x2 + 18x 24x4 – 12x2 + 18x = 6x 6x 6x 6x = 6x(4x3 – 2x + 3)  = 24x4 – 12x2 + 18x

  5. 9.5 Common Factors Finding Factors of a Polynomial Write the following as the products of factors: 6x3+ 3x2 + 9x 6x3 + 3x2 + 9x = 3x 3x 3x 3x = 3x(2x2 + x+ 3) 6r4 + 10r3 – 14r2 6r4 + 10r3 – 14r2 = 2r2 2r2 2r2 2r2 = 2r2(3r2 + 5r– 7)

  6. 9.5 Common Factors Finding Factors of a Polynomial Write the following as the products of factors: 2b3+ 6b2 – 12b 2b3 + 6b2 – 12b = 2b 2b 2b 2b = 2b(b2 + 3b– 6) 4y3 – 16y2 + 8y 4y3 – 16y2 + 8y = 4y 4y 4y 4y = 4y(y2 – 4y + 2)

  7. 9.5 Common Factors Factor common binomials: r(t + 1) + s(t + 1) a(x – 3) + 6(x – 3) = (r + s) (t + 1) (x – 3) = (a + 6)

  8. 9.5 Common Factors Factor common binomials: a(b + 4) + c(b + 4) x(x + 2) – 5(x + 2) = (a + c) (b + 4) (x + 2) = (x – 5)

  9. 9.5 Common Factors Key Skills Factor a polynomial by grouping. Factor 3x2 + 3x + 7x + 7by grouping. 3x2 + 3x + 7x + 7 = (3x2 + 3x) + (7x + 7) = 3x(x + 1) + 7(x + 1) = (3x + 7)(x + 1)

  10. 9.5 Common Factors Factor by grouping: x2 + 2x + 3x + 6 x2– 3x + 10x – 30 (x2 + 2x) + (3x + 6) (x2 – 3x) + (10x – 30) x(x + 2) + 3(x + 2) x(x – 3) + 10(x – 3) = (x + 2)(x + 3) = (x – 3)(x + 10)  (x + 2)(x + 3)  (x – 3)(x + 10) x2 + 3x + 2x + 6 x2 + 10x – 3x – 30

  11. 9.5 Common Factors Factor by grouping: x2 + 6x + 7x + 42 x2 + 4x + 5x + 20 (x2 + 6x) + (7x + 42) (x2 + 4x) + (5x + 20) x(x + 6) + 7(x + 6) x(x + 4) + 5(x + 4) = (x + 6)(x + 7) = (x + 4)(x + 5)

  12. 9.5 Common Factors Factor by grouping: 6x2+ 9x – 6x – 9 6x2 + 9x – 6x – 9 (6x2– 6x) + (9x – 9) (6x2 + 9x) + (–6x – 9) 6x(x – 1) + 9(x – 1) 3x(2x + 3) –3(2x + 3) = (x – 1)(6x + 9) = (2x + 3)(3x – 3)

  13. 9.5 Common Factors Factor by grouping: 8x2+ 12x + 4x + 6 8x2 + 12x + 4x + 6 (8x2 + 4x) + (12x + 6) (8x2 + 12x) + (4x + 6) 4x(2x + 1) + 6(2x + 1) 4x(2x + 3) + 2(2x + 3) = (2x + 1)(4x + 6) = (2x + 3)(4x + 2)

  14. 9.5 Common Factors Factor by grouping: 6x2 + 15x – 8x – 20 3x2– 21x + 5x – 35 (6x2– 8x) + (15x – 20) (3x2– 21x) + (5x – 35) 2x(3x – 4) + 5(3x – 4) 3x(x – 7) + 5(x – 7) = (3x – 4)(2x + 5) = (x – 7)(3x + 5)

  15. 9.5 Common Factors Factor by grouping: 3x2 + 12x – 2x – 8 4ax – bx + 4ay – by (3x2 + 12x) + (– 2x – 8) (4ax + 4ay) + (–bx – by) 3x(x + 4) – 2(x + 4) 4a(x + y) – b(x + y) = (3x – 2)(x + 4) = (4a – b)(x + y) 6m3 + 4m – 9m2 – 6 (6m3 + 4m) + (– 9m2 – 6) 2m(3m2 + 2) – 3(3m2+ 2) = (3m2 + 2)(2m – 3)

  16. 9.5 Common Factors Factor by grouping: ax + bx – ay – by ax + bx + ay + by (ax + bx) + (–ay – by) (ax + bx) + (ay + by) x(a + b) – y(a + b) x(a + b) + y(a + b) = (x – y)(a + b) = (a + b)(x + y) = (a + b)(x – y)  (a + b)(x + y)  (a + b)(x – y) ax + ay + bx + by ax – ay + bx – by ax + bx + ay + by ax + bx – ay – by

More Related