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Factoring by grouping

Factoring by grouping. MM1A2f: FACTOR Essential Question: What are my roots?. Warm-up: Factoring Practice x-factor: multiply to top #, add to bottom #. 1. 2 . 3 . 4 . -24. -36. 24. 7. -8. 3. -9. 4. 7. 1. -6. -4. -5. -5. 8. -10. 8 . 5 . 6 . 7. -18. 3. -21. 35. -3.

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Factoring by grouping

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  1. Factoring by grouping MM1A2f: FACTOR Essential Question: What are my roots?

  2. Warm-up: Factoring Practicex-factor: multiply to top #, add to bottom # 1. 2. 3. 4. -24 -36 24 7 -8 3 -9 4 7 1 -6 -4 -5 -5 8 -10 8. 5. 6. 7. -18 3 -21 35 -3 -1 -6 3 -7 3 -7 -5 -4 -3 -4 -12

  3. Factoring by Grouping • Factor a common monomial, then look for a common binomial • ???? Do we remember monomials & binomials???

  4. Factor out common binomial • EX1: 5x2(x – 2) – 3(x – 2) distributive property to factor (5x2 – 3)(x – 2) • EX2: 7y(5 – y) + 3(y – 5) factor out -1 -7y(y – 5) + 3(y – 5) distributive property to factor (-7y + 3)(y – 5)

  5. Factor by Grouping • EX3: m3 + 7m2 – 2m – 14 Group (m3 + 7m2) + (-2m – 14) Factor each group m2(m + 7) + -2(m + 7) Distributive property (m2 – 2)(m + 7)

  6. Factor by Grouping • EX4: n3 + 30 + 6n2 + 5n Rearrange terms n3 + 6n2 + 5n + 30 Group terms (n3 + 6n2) + (5n + 30) Factor each group n2(n + 6) + 5(n + 6) Distributive Property (n2 + 5) (n + 6)

  7. Factor Completely • EX5: 5x3 – 55x2 + 90x Factor GCF 5x(x2 – 11x + 18) Factor (x-factor) 5x(x – 9)(x – 2) • EX6: 48y4 – 3y2 Factor GCF 3y2(16y2 – 1) Factor (special Product) 3y2(4y – 1)(4y + 1)

  8. Solve a Polynomial Equation • EX7: 7x3 + 14x2 = 105x Rearrange Equation 7x3 + 14x2 – 105x = 0 Factor GCF 7x(x2 + 2x – 15) = 0 Factor (x – factor) 7x(x + 5)(x – 3) = 0 Zero Product Prop. 7x = 0 x+5 = 0 x – 3 =0 x = 0 x = -5 x = 3

  9. You Try…. • 11x(x-8) + 3(x-8)9x3+9x2 – 7x – 7 • 4x3 – 36x 2y3 – 16y2 + 32y • 10x3 + 21y - 35x2 - 6xy

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