1. Solving Quadratics: Factoring

2. What is a factor? Numbers you can multiply to get another number 2  3

3. Factoring Polynomials This process is basically the REVERSE of the distributive property. distributive property factoring Factored formStandard form

4. In factoring you start with a polynomial and you want to rewrite it as a product. Factoring Polynomials Three terms Factored form

5. Techniques of Factoring Polynomials 1. Always look for the Greatest Common Factor (GCF) first.

6. Standard Form of Quadratic Equations

7. 2. Factoring Trinomials. Is there a GCF? Techniques of Factoring Polynomials New Method: product of two binomials (x+ )(x+ )

8. 2. Factoring Trinomials. We need to find factors of a  c ….that add up to b Techniques of Factoring Polynomials

9. Examples

12. General Forms

13. Examples

16. Difference of two squares

18. Note… Not every quadratic expression can be factored into two factors. For example x 2 – 7x + 13. We may easily see that there are no factors of 13 that added up give us –7 x 2 – 7x + 13 is a prime trinomial.

19. Your Turn!

20. Factoring the Difference of Two Squares The difference of two bases being squared, factors as the product of the sum and difference of the bases that are being squared. a 2 – b 2 = (a + b)(a – b) FORMULA: (a + b)(a – b) = a 2 – ab + ab – b 2 = a 2 – b 2

21. Factoring the difference of two squares Factor x 2 – 4y 2 Factor 16r 2 – 25 (x) 2 (2y) 2 (x – 2y)(x + 2y) Now you can check the results… (4r) 2 (5) 2 Difference of two squares Difference Of two squares (4r – 5)(4r + 5) a 2 – b 2 = (a + b)(a – b)

22. Difference of two squares