7.3 Special Factoring Techniques What are your objectives for Section 7.3? How can you accomplish each objective? 1 Factor a Perfect Square Trinomial • Learn the formula for Factoring a Perfect Square Trinomial. • Review all of the perfect squares. • Always begin by asking yourself, “Can I factor out a GCF?” and, after factoring, always ask yourself, “Can I factor again?” • Complete the given examples on your own. • Complete You Try 1. 2 Factor the Difference of Two Squares • Learn the formula for Factoring the Difference of Two Squares. • Always begin by asking yourself, “Can I factor out a GCF?” and, after factoring, always ask yourself, “Can I factor again?” • Recognize the difference between the sum of two squares and the difference of two squares. • Complete the given examples on your own. • Complete You Trys 2 and 3. 3 Factor the Sum and Difference of Two Cubes • Learn the formula for Factoring the Sum and Difference of Two Cubes. • Review all the perfect cubes. • Always begin by asking yourself, “Can I factor out a GCF?” and, after factoring, always ask yourself, “Can I factor again?” • Complete the given examples on your own. • Complete You Trys 4 and 5. Read the explanations, follow the examples, take notes, and complete the You Trys. 1 Factor a Perfect Square Trinomial Recall that we can square a binomial using the formulas (a b)2 a2 2ab b2 (a b)2 a2 2ab b2 For example, (x 5)2 x2 2x(5) 52 x2 10x 25. Since factoring a polynomial means writing the polynomial as a product of its factors, x2 10x 25 factors to (x 5)2. The expression x2 10x 25 is a perfect square trinomial. A perfect square trinomial is a trinomial that results from squaring a binomial. We can use the factoring method presented in Section 7.2 to factor a perfect square trinomial, or we can learn to recognize the special pattern that appears in these trinomials. Above we stated that x2 10x 25 factors to (x 5)2. How are the terms of the trinomial and binomial related? Compare x2 10x 25 to (x 5)2. x2 is the square of x, the fi rst term in the binomial. 25 is the square of 5, the last term in the binomial. Write out the definition of a perfect square trinomial using your own words. 378 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
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