Warm Up

1. Warm Up • 1.) What is the factored form of 2x2 + 9x + 10? • 2.) What is the factored form of 6x2 – 23x – 4?

2. 8.7 Factoring Special Cases

3. Objective • Factor perfect-square trinomials and the differences of two squares

4. Factoring Perfect Square Trinomials • “Reversing” the rules for multiplying special case binomials will result in the original factors. • Any trinomial of the form a2 + 2ab + b2 or a2 -2ab + b2 is a perfect square trinomial because it is the result of squaring a binomial. • For every real number a and b: • a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2 • x2 + 8x + 16 = (x + 4)(x + 4) = (x + 4)2 • a2 – 2ab + b2 = (a – b)(a – b) = (a – b)2 • 4n2 – 12n + 9 = (2n – 3)(2n – 3) = (2n – 3)2

5. Example 1 – Factoring a Perfect-Square Trinomial • What is the factored form of x2 – 4x +4?

6. Extra Example 1 • What is the factored form of x2 + 6x + 9?

7. Example 2 – Factoring to Find a Length • Suppose the area of a square can be represented by the expression 9x2 + 24x + 16. What is an expression for the length of one side of the square?

8. Difference of Two Squares • You can factor a difference of squares, a2 – b2, as (a + b)(a – b) • For all real numbers a and b: • a2 – b2 = (a + b)(a – b) • Ex.: • x2 – 64 = (x + 8)(x – 8) • 25x2 – 36 = (5x + 6)(5x – 6)

9. Example 3 – Factoring a Difference of Two Squares • What is the factored form of x2 – 64?

10. Extra Example 3 • What is the factored form of x2 – 100?

11. Example 4 – Factoring a Difference of Two Squares • What is the factored form of 9x2 – 25?

12. Extra Example 4 • What is the factored form of 25d2 – 64?

13. Example 5 – Factoring Out a Common Factor • What is the factored form of 12x2 – 3?

14. Assignment • Pg. 514 – 515 (9 – 17 all, 24 – 32 all, 36 – 41 all)