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### Presentation2

1. 1. MATH<br />Factoring<br />
2. 2. AGENDA<br /><ul><li>Terms with Common Factors
3. 3. Factoring the form x²+bx+c
4. 4. Factoring the form ax²+bx+c
5. 5. Special Factorizations</li></ul>Math<br />
6. 6. Review<br /><ul><li>What is a Factor?
7. 7. How do you FOIL?
8. 8. EX: (x – 2)(x + 3)
9. 9. Solution: x2 + x - 6</li></ul>M<br />H<br />A<br />T<br />
10. 10. Terms With Common Factors<br /><ul><li>Key words…Common, Factors (Bittinger, pg. 23)
11. 11. Ex: Factor out Greatest Common Factor... </li></ul>4x – 8<br />9x + 108 <br />5/4 x + 5/2 <br />3x+ 9<br />
12. 12. Terms with Common Factors<br /><ul><li>Solutions:</li></ul>4 (x -2)<br />9 (x – 12)<br />5/4 (x + 2)<br />3x + 9<br /> 3(x + 3)<br />
13. 13. Factoring the form x²+bx+c<br />EX: x² + 5x + 6<br />(x _ _) (x _ _)<br />Ex:<br />x2 – x – 30<br />2x2 – 16x + 32<br />x² + 6x +3<br />
14. 14. Factoring the form x²+bx+c<br />Solutions:<br />(x + 5)(x – 6)<br />(2x – 8)(x – 4)<br />x² + 7x +12 =<br />(x + 3)(x +4)<br />
15. 15. Factoring The form ax²+bx+c<br />The FOIL method! (Bittinger, pg. 26)<br />Factor out largest common factor<br />Find product of ax²<br />Find product of c <br />Keep trying until you can FOIL to f(x) <br />EX:<br />3x² + 19x + 20<br />4x² - 12x + 16<br />¾ x² - 17/4 x - 14<br />4x² + 8x + 4 <br />
16. 16. Factoring The form ax²+bx+c<br />Solutions:<br />(3x + 4)(x + 5)<br />4(x – 4)(x + 1)<br />( x – 2)( 3x +7)<br />4x² + 10x + 6<br />2(2x+3)(x+1)<br />1<br />4<br />
17. 17. Factoring The form ax²+bx+c<br />The Grouping Method (Bittinger, pg. 27-28)<br />Factor first<br />Multiply by the leading coefficient a with the constant<br />Try to factor so that the sum of the factors of a c equal the middle term.<br />Split the middle term using the answers just found<br />Factor by grouping<br />EX: 12x3 + 10x2 – 8x<br />Knowledge<br />.<br />
18. 18. Factoring The form ax²+bx+c<br />More Ex:<br />108x2 + 288x + 144<br />5x3 - 5x<br />Solutions:<br />36(3x + 2)(x + 2)<br />5x(x – 1)(x + 1)<br />Knowledge<br />
19. 19. Special Factorizations<br />Difference of squares (Bittinger, pg. 28)<br />A2 – B2 = (A + B)(A – B)<br />EX:<br />x2 – 16<br />36x2 – 25 <br />Solutions<br />(x – 4)(x + 4)<br />(6x – 5)( 6x + 5)<br />Knowledge<br />
20. 20. Special Factorizations<br />Same Squares (Bittinger, pg. 29)<br />A2 + 2AB + B2 = (A + B)2<br />A2 – 2AB + B2 = (A – B)2<br />EX:<br />x2 + 16x + 64<br />25x2 – 30x + 9<br />Solutions:<br />(x + 8)2<br />(5x – 3)2<br />Knowledge<br />
21. 21. Special Factorizations<br />Sum or Difference of Cubes (Bittinger, pg. 29)<br />A3 + B3 = (A + B)(A2 – AB + B2)<br />A3 – B3 = (A – B)(A2 + AB + B2)<br />Ex: Factor<br />x3 – 8<br />16x3 - 250<br />Solutions:<br />(x- 2)(x2 + 2x + 4)<br />2(2x – 5)(4x2 + 10x + 25)<br />Knowledge<br />
22. 22. Overall Steps to Factoring<br />The Steps (Bittinger, pg. 30)<br />Factor out the largest common factor<br />Look at a # of terms<br />Two Terms<br />Three Terms<br />Four + terms<br />Factor COMPLETELY!<br />I learned <br /> Math…<br />
23. 23. Reference<br />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. <br />I think…<br />Maybe…<br />Possibly…???<br />
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