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Published byJane Jordan Modified over 6 years ago
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Warm Up 1.) What is the factored form of 2x2 + 9x + 10? 2.) What is the factored form of 6x2 – 23x – 4?
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8.7 Factoring Special Cases
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Objective Factor perfect-square trinomials and the differences of two squares
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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
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Example 1 – Factoring a Perfect-Square Trinomial
What is the factored form of x2 – 4x +4?
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Extra Example 1 What is the factored form of x2 + 6x + 9?
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Example 2 – Factoring to Find a Length
Suppose the area of a square can be represented by the expression 9x2 + 24x What is an expression for the length of one side of the square?
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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)
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Example 3 – Factoring a Difference of Two Squares
What is the factored form of x2 – 64?
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Extra Example 3 What is the factored form of x2 – 100?
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Example 4 – Factoring a Difference of Two Squares
What is the factored form of 9x2 – 25?
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Extra Example 4 What is the factored form of 25d2 – 64?
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Example 5 – Factoring Out a Common Factor
What is the factored form of 12x2 – 3?
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Assignment Pg. 514 – 515 (9 – 17 all, 24 – 32 all, 36 – 41 all)
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