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Warm-Up 2.5 Factor the GCF out of each. 8x 4 – 14x 3 + 20x 2 – 44x 9x 3 y + 18x 4 y 2 – 3xy

Warm-Up 2.5 Factor the GCF out of each. 8x 4 – 14x 3 + 20x 2 – 44x 9x 3 y + 18x 4 y 2 – 3xy. = 2x(4x 3 – 7x 2 + 10x – 22) . = 3xy(3x 2 + 6x 3 y – 1). Algebra 3 Lesson 2.5 Objective: SSBAT factor a polynomial using grouping. Standards: M11.D.2.2.2. Factoring by Grouping

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Warm-Up 2.5 Factor the GCF out of each. 8x 4 – 14x 3 + 20x 2 – 44x 9x 3 y + 18x 4 y 2 – 3xy

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  1. Warm-Up 2.5 Factor the GCF out of each. 8x4 – 14x3+ 20x2 – 44x 9x3y + 18x4y2 – 3xy = 2x(4x3 – 7x2 + 10x – 22) = 3xy(3x2 + 6x3y – 1)

  2. Algebra 3 • Lesson 2.5 • Objective: • SSBAT factor a polynomial using grouping. Standards: M11.D.2.2.2

  3. Factoring by Grouping • Use when the other methods will not work • Can use this method if you are able to split the polynomial into groups that contain a GCF within each group

  4. Steps for Factoring by Grouping Split the polynomial into 2 or more groups so that each group has a GCF. Factor out the GCF of each group formed. The expressions left behind in each should be identical (if not you can not factor the polynomial). If so, the identical expression will be one parenthesis and the grouping of the GCFs will be the other parenthesis.

  5. Examples: Factor each by grouping. 10xy + 14x + 15y + 21 = (10xy + 14x) + (15y + 21) = 2x(5y + 7) + 3(5y + 7) = (2x + 3)(5y + 7)

  6. 2. 4x3 + 5x2 – 24x – 30 = (4x3 + 5x2) + (-24x – 30) = x2(4x + 5) – 6(4x + 5) = (x2 – 6)(4x + 5)

  7. 3. 4m4 – 16m3 + m – 4 = (4m4– 16m3) + (m – 4) = 4m3(m – 4) + 1(m – 4) = (4m3 + 1)(m – 4)

  8. 4. 8x + 48 + 18z + 3xz = (8x + 48) + (18z + 3xz) = 8(x + 6) + 3z(6 + x) = 8(x + 6) + 3z(x + 6) = (8 + 3z)(x + 6)

  9. 5. 18a2 – 12ac – 21ab + 14bc = (18a2 – 12ac) + (-21ab + 14bc) = 6a(3a – 2c) – 7b(3a – 2c) = (6a – 7b)(3a – 2c)

  10. 6. 4xy – 20x + 3y – 21 = (4xy – 20x) + (3y – 21) = 4x(y – 5) + 3(y – 7) Can not be factored. Prime.

  11. On Your Own. Factor by Grouping. 9mn – 6n + 12m – 8 = (3m – 2)(3n + 4)

  12. Homework Worksheet 2.5

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