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Bell Ringer: 10/22/08

Bell Ringer: 10/22/08. What is the greatest common factor for 64 and 120? Solve: Factor:. 3) (4x + 11)(4x – 11). 1) 8. 2) 4. Identity 3:. Cube of a sum. Multiplying Cubes. Using the Rule: (x + 2) 3 = (x + 2) (x + 2) (x + 2). Cube the first term. Cube the last term.

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Bell Ringer: 10/22/08

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  1. Bell Ringer: 10/22/08 • What is the greatest common factor for 64 and 120? • Solve: • Factor: 3) (4x + 11)(4x – 11) 1) 8 2) 4

  2. Identity 3: Cube of a sum

  3. Multiplying Cubes • Using the Rule: (x + 2)3 = (x + 2) (x + 2) (x + 2) Cube the first term Cube the last term Square last term & multiply by 3 Multiply the last term by 3

  4. (x + 2)(x + 2)(x + 2) (x2 + 4x + 4)(x + 2) x2 •x = x3 x2• 2 = 2x2 4x • x = 4x2 4x • 2 = 8x 4 • x = 4x 4 • 2 = 8 Expand the cubic Use Identity 2 to multiply the first two binomials Using the distributive property multiply the rest Using the slightly longer way  = 6x2 X3 + 6x2 + 12x + 8 = 12x

  5. Undo Divide by 3 & square root Cube root the first term Cube root the last term Divide by 3 4 (x – 4)(x – 4)(x – 4) = (x – 4)3

  6. Identity 5: Cube of a difference

  7. Multiplying Cubes • Using the Rule: (x - 3)3 = (x - 3) (x - 3) (x - 3) Cube the first term Cube the last term Square last term & multiply by 3 Multiply the last term by 3

  8. (x - 3)(x - 3)(x - 3) (x2 - 6x + 9)(x - 3) x2 •x = x3 x2• -3 = -3x2 -6x • x = -6x2 -6x • -3 = 18x 9 • x = 9x 9 • -3 = -27 Expand the cubic Use Identity 2 to multiply the first two binomials Using the distributive property multiply the rest Using the slightly longer way  = -9x2 X3 - 9x2 + 27x - 27 = 27x

  9. Undo Divide by 3 & square root Cube root the first term Cube root the last term Divide by 3 5 (x – 5)(x – 5)(x – 5) = (x – 5)3

  10. Try a few on your own from the practice sheet • (x – 3)3 • (x – 5)3 • (x – 4)3 • (x – 2)3 • (x + 2)3

  11. Now let’s try one of these:

  12. What identity does it match? • Is there any number or letter in common with all three terms? • Divide all three terms by this greatest common factor 3n Now which identity does the trinomial match?

  13. Do these two terms have a common number or variable? 4x3

  14. 2a2 • Do these three terms have a GCF? • Now factor the trinomial • 2a2(a – 6)(a – 9)

  15. Try this one on your own • Complete the front page only of the practice sheet

  16. GCF can help us with other cubic polynomials. Group the first two terms together and group the last two terms together Find the GCF of each group

  17. GCF can help us with other cubic polynomials. Group the first two terms together and group the last two terms together Find the GCF of each group

  18. GCF can help us with other cubic polynomials. Group the first two terms together and group the last two terms together Find the GCF of each group

  19. GCF can help us with other cubic polynomials. Group the first two terms together and group the last two terms together Find the GCF of each group

  20. Summarizer Factor and tell which method you used. Why did you use that method?

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