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Objective: The learner will..,

9.5 Common Factors. Objective: The learner will..,. NCSCOS. Factor a polynomial using the greatest common factor (GCF). Factor a polynomial into two binomials by finding the common binomial method. 1.01, 4.02. 9.5 Common Factors. Factor using the GCF. 3x 2 – 15x.

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Objective: The learner will..,

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  1. 9.5 Common Factors Objective: The learner will.., NCSCOS • Factor a polynomial using the greatest common factor (GCF). • Factor a polynomial into two binomials by finding the common binomial method. • 1.01, 4.02

  2. 9.5 Common Factors Factor using the GCF 3x2 –15x 14a2 – 4a = 3x(x – 5) = 2a(7a – 2) 5am – 10an 8x2 + 24x = 5a(m – 2n) = 8x(x + 3) 6ab – 3a 5x2yz + 10y2z = 3a(2b – 1) = 5yz(x2 + 2y)

  3. 9.5 Common Factors Solve by: finding the GCF xn+3 + xn x3n+21 + 2x2n+14 xnx3 + xn x3nx21 + 2x2nx14 xn(x3 + 1) x3nx14x7 + 2x2nx14 x2n+14(xn+7 + 2) 9x2n + 21x2n+1 9x2n + 21x2nx1 3x2n(3 + 7x)

  4. 9.5 Common Factors Factor using the GCF 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)

  5. 9.5 Common Factors Factor using the GCF 2b3 + 6b2 – 12b = 2b(b2 + 3b– 6) 2b 4y3 – 16y2 + 8y = 4y(y2 – 4y + 2) 4y 6a8 – 30a6 + 12a4 = 6a4(a4 – 5a2 + 2) 6a4

  6. 9.5 Common Factors Factor using the GCF 20x4 – 12x3 + 8x2 = 4x2(5x2 – 3x + 2) 4x2 24x4 – 12x2 + 18x = 6x(4x3 – 2x + 3) 6x 2x3y – 8x2y2 + 17xy3 = xy(2x2 – 8xy + 17y2) xy

  7. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: ax – 3a + 6x – 18 rt + r + st + s (ax – 3a) + (6x – 18) (rt + r) + (st + s) a(x – 3) + 6(x – 3) r(t + 1) + s(t + 1) (x – 3) = (a + 6) = (r + s) (t + 1)

  8. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: x2 + 2x – 5x – 10 ab + 4a + bc + 4c (x2 + 2x) + (–5x – 10) (ab + 4a) + (bc + 4c) x(x + 2) – 5(x + 2) a(b + 4) + c(b + 4) (x + 2) = (x – 5) = (a + c) (b + 4)

  9. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: ax + bx + ay + by 4ab + 8b + 3a + 6 (ax + bx) + (ay + by) (4ab + 8b) + (3a + 6) x(a + b) + y(a + b) 4b(a + 2) + 3(a + 2) = (x + y)(a + b) = (4b + 3)(a + 2)

  10. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: x2– 3x + 10x – 30 x2 + 2x + 3x + 6 (x2 + 2x) + (3x + 6) (x2 – 3x) + (10x – 30) x(x + 2) + 3(x + 2) x(x – 3) + 10(x – 3) = (x + 3)(x + 2) = (x + 10)(x – 3)

  11. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 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 + 7)(x + 6) = (x + 5)(x + 4)

  12. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 6x2 + 4x – 9x – 6 3x2 + 3x + 7x + 7 = (6x2 + 4x) + (–9x – 6) = (3x2 + 3x) + (7x + 7) = 2x(3x + 2) – 3(3x + 2) = 3x(x + 1) + 7(x + 1) = (2x – 3)(3x + 2) = (3x + 7)(x + 1)

  13. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 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) = (6x + 9)(x – 1) = (3x – 3)(2x + 3)

  14. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 8x2 + 12x + 4x + 6 8x2+ 12x + 4x + 6 (8x2 + 12x) + (4x + 6) (8x2 + 4x) + (12x + 6) 4x(2x + 3) + 2(2x + 3) 4x(2x + 1) + 6(2x + 1) = (4x + 2)(2x + 3) = (4x + 6)(2x + 1)

  15. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 3x2– 21x + 5x – 35 3x2– 21x + 5x – 35 (3x2+ 5x) + (–21x – 35) (3x2– 21x) + (5x – 35) x(3x + 5) – 7(3x + 5) 3x(x – 7) + 5(x – 7) = (x – 7)(3x + 5) = (3x + 5)(x – 7)

  16. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 6x2– 15x – 8x + 20 4x2 + 14x + 6x + 21 (6x2– 8x) + (–15x + 20) (4x2 + 6x) + (14x + 21) 2x(3x – 4) – 5(3x – 4) 2x(2x + 3) + 7(2x + 3) = (2x + 7)(2x + 3) = (2x – 5)(3x – 4)

  17. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 18x2– 30x – 3x + 5 12x2 + 9x + 8x + 6 (18x2– 3x) + (–30x + 5) (12x2 + 9x) + (8x + 6) 3x(6x – 1) – 5(6x – 1) 3x(4x + 3) + 2(4x + 3) = (3x – 5)(6x – 1) = (3x + 2)(4x + 3)

  18. 9.5 Common Factors Solve by: (1) Grouping, (2) find the greatest common factor (GCF), (3) find the common binomial (CB) and other binomial: 10x2– 14xy – 15x + 21y (10x2– 15x) + (–14xy + 21y) 5x(2x – 3) – 7y(2x – 3) 4ax + 3ay + 4bx + 3by = (5x – 7y)(2x – 3) (4ax + 4bx) + (3ay + 3by) 4x(a + b) + 3y(a + b) = (4x + 3y)(a + b)

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