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March 26

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  • 1. 1 Today: Factoring (ax2 + bx + c) Trinomials Review of all other factoring methods/test review Class Work
  • 2. 2 Complete Factoring Guide Available
  • 3. 3 Review: Perfect Square Trinomial (x² + 8x + 16) Remember, a PST factors into either a square of a sum or a square of a difference. Use the FOIL method to factor the following: (x² + 4x + 4x + 16) = (x + 4)² (x² - 16x + 64) (x² - 8x - 8x + 64) = (x - 8)² (x² - 15x + 36) (x² - 12x - 3x + 36) = Is not a sp. product. A trinomial with first & third term squares is only a PST if... 9y3 + 12x2 + 4x PST or no PST?
  • 4. Steps in factoring completely: 1. Look for the GCF 2. Look for special cases. a. difference of two squares b. perfect square trinomial 3. If a trinomial is not a perfect square, look for two different binomial factors.  8t4 – 32t3 + 40t = 8t(t3 - 4t + 5)  4x2 – 9y2 = (2x)2 – (3y)2  x2 + 8x + 16 = x2 + 8x + 42 = (x + 4)2  x2 + 11x – 10 = (x + 10)(x – 1)
  • 5. An organized approach to factoring 2nd degree trinomials 5 Factoring (ax2 + bx + c) Trinomials
  • 6. Factoring Trinomials  Use this algorithm (procedure) to take the guesswork out of factoring trinomials.  It would be a good idea to write the steps down once, as they are easy to forget when away from class  You can use these steps for any ax2 + bx + c polynomial, and for any polynomial you are having difficulty factoring.
  • 7. Step 1 7 Multiply the leading coefficient and the constant term
  • 8. Step 2 8 Find the two factors of 24 that add to the coefficient of the middle term. Notice the 'plus, plus' signs in the original trinomial. Factors of 24: 1 24 2 12 3 8 4 6 Our two factors are 4 & 6
  • 9. Step 3 9 Re-write the original trinomial and replace 10x with 6x + 4x. 3x2 + 6x + 4x + 8 Step 4 Factor by Grouping
  • 10. Step 5 10 Factor out the GCF of each pair of terms After doing so, you will have... Step 6 Factor out the common binomial, check that no further factoring is possible, and the complete factorization is..
  • 11. 11 Practice(2) Factor: 6x3 + 14x2 + 8x Factor: 4x2 – 20x + 25
  • 12. 9y3 + 12x2 + 4x Factor 3x5 – 243xFactor 2m2 – 20mn + 50n2 Factor 5x4y – 80x2y3 Factor 5x – 5y + ax - ay