YOU TRY 1 b) From 4t3 32t 2 64t we can begin by taking out the GCF of 4t. 4t3 32t2 64t 4t(t2 8t 16) What do you square to get t2? t (t)2 (4)2 What do you square to get 16? 4 Does the middle term of the trinomial in parentheses equal 2 t 4? Yes. 2 t 4 8t. 4t3 32t2 64t 4t(t2 8t 16) 4t(t 4)2 Check by multiplying. c) We cannot take out a common factor. Since the fi rst and last terms of 9w2 12w 4 are perfect squares, let’s see whether this is a perfect square trinomial. 9w2 12w 4 What do you square to get 9w2? 3w (3w)2 (2)2 What do you square to get 4? 2 Does the middle term equal 2 3w 2? Yes. 2 3w 2 12w. Therefore, 9w2 12w 4 (3w 2)2. Check by multiplying. d) We cannot take out a common factor. The fi rst and last terms of 4c2 20c 9 are perfect squares. Is this a perfect square trinomial? 4c2 20c 9 What do you square to get 4c2? 2c (2c)2 (3)2 What do you square to get 9? 3 Does the middle term equal 2 2c 3? No! 2 2c 3 12c. This is not a perfect square trinomial. Applying a method from Section 7.3, we fi nd that the trinomial does factor, however. 4c2 20c 9 (2c 9)(2c 1). Check by multiplying. Factor completely. a) g2 14g 49 b) 6y3 36y2 54y c) 25v2 10v 1 d) 9b2 15b 4 2 Factor the Difference of Two Squares Another common factoring problem is a difference of two squares. Some examples of these types of binomials are 64 t2 c2 36 49x2 25y2 h4 16 Notice that in each binomial, the terms are being subtracted, and each term is a perfect square. In Section 6.2, Multiplication of Polynomials, we saw that (a b)(a b) a2 b2 If we reverse the procedure, we get the factorization of the difference of two squares. www.mhhe.com/messersmith SECTION 7.4 Factoring Special Trinomials and Binomials 415
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above