7.4 Factoring Special Trinomials and Binomials What are your objectives for Section 7.4? How can you accomplish each objective? 1 Factor a Perfect Square Trinomial • Notice, again, that factoring is the opposite of multiplication. • Learn the formula for Factoring a Perfect Square Trinomial. • Complete the given examples on your own. • Complete You Try 1. 2 Factor the Difference of Two Squares • Notice, again, that factoring is the opposite of multiplication. • Learn the formula for Factoring the Difference of Two Squares. • Complete the given examples on your own. • Complete You Trys 2 and 3. 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 3)2 x2 2x(3) 32 x2 6x 9. Since factoring a polynomial means writing the polynomial as a product of its factors, x2 6x 9 factors to (x 3)2. The expression x2 6x 9 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. How are the terms of x2 6x 9 and (x 3)2 related? x2 is the square of x, the fi rst term in the binomial. 9 is the square of 3, the last term in the binomial. We get the term 6x by doing the following: 6x 2 x 3 Q c a Two First term Last term in binomial times in binomial www.mhhe.com/messersmith SECTION 7.4 Factoring Special Trinomials and Binomials 413
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above