The document provides an agenda for learning about factoring polynomials. It discusses factoring terms with common factors, factoring quadratics in the forms x^2 + bx + c and ax^2 + bx + c using FOIL. It also covers special factorizations including difference of squares, same squares, and sum and difference of cubes. The steps for factoring include factoring out the greatest common factor, examining the number of terms, and factoring completely. Examples are provided for each topic along with the factorized solutions.

1. MATH Factoring

3. Factoring the form x²+bx+c

4. Factoring the form ax²+bx+c

5. Special FactorizationsMath

7. How do you FOIL?

8. EX: (x – 2)(x + 3)

9. Solution: x2 + x - 6M H A T

11. Ex: Factor out Greatest Common Factor... 4x – 8 9x + 108 5/4 x + 5/2 3x+ 9

13. Factoring the form x²+bx+c EX: x² + 5x + 6 (x _ _) (x _ _) Ex: x2 – x – 30 2x2 – 16x + 32 x² + 6x +3

14. Factoring the form x²+bx+c Solutions: (x + 5)(x – 6) (2x – 8)(x – 4) x² + 7x +12 = (x + 3)(x +4)

15. Factoring The form ax²+bx+c The FOIL method! (Bittinger, pg. 26) Factor out largest common factor Find product of ax² Find product of c Keep trying until you can FOIL to f(x) EX: 3x² + 19x + 20 4x² - 12x + 16 ¾ x² - 17/4 x - 14 4x² + 8x + 4

16. Factoring The form ax²+bx+c Solutions: (3x + 4)(x + 5) 4(x – 4)(x + 1) ( x – 2)( 3x +7) 4x² + 10x + 6 2(2x+3)(x+1) 1 4

17. Factoring The form ax²+bx+c The Grouping Method (Bittinger, pg. 27-28) Factor first Multiply by the leading coefficient a with the constant Try to factor so that the sum of the factors of a c equal the middle term. Split the middle term using the answers just found Factor by grouping EX: 12x3 + 10x2 – 8x Knowledge .

18. Factoring The form ax²+bx+c More Ex: 108x2 + 288x + 144 5x3 - 5x Solutions: 36(3x + 2)(x + 2) 5x(x – 1)(x + 1) Knowledge

19. Special Factorizations Difference of squares (Bittinger, pg. 28) A2 – B2 = (A + B)(A – B) EX: x2 – 16 36x2 – 25 Solutions (x – 4)(x + 4) (6x – 5)( 6x + 5) Knowledge

20. Special Factorizations Same Squares (Bittinger, pg. 29) A2 + 2AB + B2 = (A + B)2 A2 – 2AB + B2 = (A – B)2 EX: x2 + 16x + 64 25x2 – 30x + 9 Solutions: (x + 8)2 (5x – 3)2 Knowledge

21. Special Factorizations Sum or Difference of Cubes (Bittinger, pg. 29) A3 + B3 = (A + B)(A2 – AB + B2) A3 – B3 = (A – B)(A2 + AB + B2) Ex: Factor x3 – 8 16x3 - 250 Solutions: (x- 2)(x2 + 2x + 4) 2(2x – 5)(4x2 + 10x + 25) Knowledge

22. Overall Steps to Factoring The Steps (Bittinger, pg. 30) Factor out the largest common factor Look at a # of terms Two Terms Three Terms Four + terms Factor COMPLETELY! I learned Math…

23. Reference Bittinger, M. L., Beecher, J. A., Ellenbogen, D. J., & Penna, J. A. (2009). Precalculus: Graphs & Models (4th ed., pp. 23-30). Boston: Pearson Education, Inc. I think… Maybe… Possibly…???