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

8.7 Factoring Special Cases

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

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

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

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

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?

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)

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

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

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

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

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

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