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Objectives

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. 9.5 Common Factors. Factor using the GCF. 6ab – 3a. = 3a(2b – 1). 5am – 5an.

marny-cook
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Objectives

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  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

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