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- 3. Factoring the form x²+bx+c
- 4. Factoring the form ax²+bx+c
- 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…???