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Warm up

Warm up. Factor 7x 3 – 28x 2 4m 3 – 20m 8y 3 – 20y 2 + 12y. 7x 2 (x – 4). 4m(m 2 – 5). 4y(2y 2 – 5y + 3). EQ: How do I factor a sum or difference of 2 cubes?. Pattern: Sum and Difference of 2 Cubes. a 3 + b 3 = (a + b) (a 2 – ab + b 2 ) a 3 – b 3 = (a – b) (a 2 + ab + b 2 )

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Warm up

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  1. Warm up Factor 7x3 – 28x2 4m3 – 20m 8y3 – 20y2 + 12y 7x2(x – 4) 4m(m2 – 5) 4y(2y2 – 5y + 3)

  2. EQ: How do I factor a sum or difference of 2 cubes?

  3. Pattern: Sum and Difference of 2 Cubes a3 + b3 = (a + b) (a2 – ab + b2) a3 – b3 = (a – b) (a2 + ab + b2) SOAP

  4. Example 1 X3 + 27 (x + 3) (x2 – 3x + 9)

  5. Example 2 X3 + 8 (x + 2) (x2 – 2x + 4)

  6. Example 3 X3 + 125 (x + 5) (x2 – 5x + 25)

  7. Example 4 Sometimes you have to factor out a GCF first 16x5 – 250x2 2x2(8x3-125) 2x2(2x-5)(4x2+10x+25)

  8. EQ: How do we use GCF to factor 4 term polynomials?

  9. Factor By Grouping

  10. Steps to Factor by Grouping 4 terms 1. Group the 1st two terms and the 2nd two terms 2. Factor out the GCF of each group 3. Write down the common parenthesis 4. In another parenthesis, write the GCFs

  11. Example 1 x3 + 12x2 – 3x – 36 x2(x + 12) – 3(x + 12) (x + 12)(x2 – 3)

  12. Example 2 y3 – 14y2 + y – 14 (y3 – 14y2) + (y – 14) y2(y – 14) + 1(y – 14) (y – 14)(y2 + 1)

  13. Example 3 m3 – 6m2 + 2m – 12 (m3 – 6m2) + (2m – 12) m2(m – 6) + 2(m – 6) (m – 6)(m2 + 2)

  14. Example 4 p3 + 9p2 + 4p + 36 (p3 + 9p2) + (4p + 36) p2(p + 9) + 4(p + 9) (p + 9)(p2 + 4)

  15. Example 5 x3 + x2 + 5x + 5 (x3 + x2) + (5x + 5) x2(x + 1) + 5(x + 1) (x + 1)(x2 + 5)

  16. Example 6 x3 – 3x2 – 5x + 15 (x3 – 3x2) + (-5x + 15) x2(x – 3) – 5(x – 3) (x – 3)(x2 – 5)

  17. Example 7 3x3 – 3x2 + x – 1 (3x3 – 3x2) + (x – 1) 3x2(x – 1) + 1(x – 1) (x – 1)(3x2 + 1)

  18. Example 8 X3 – 2x2 – 9x + 18 (x-3)(x+3)(x-2)

  19. Example 9 X2y2- 3x2- 4y2 + 12 (x-2)(x+2)(y2-3)

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