Putting It All Together What is your objective? How can you accomplish the objective? 1 Learn Strategies for Factoring a Given Polynomial • Be sure that you can apply the techniques you have learned in the previous sections. • Know which steps to take based on how many terms are in the polynomial. • Complete the given example on your own. • Complete You Try 1. Read the explanations, follow the examples, take notes, and complete the You Trys. 1 Learn Strategies for Factoring a Given Polynomial In this chapter, we have discussed several different types of factoring problems. We have practiced the factoring methods separately in each section, but how do we know which factoring method to use if we are given many different types of polynomials together? We will discuss some strategies in this section. First, recall the steps for factoring any polynomial: Summary To Factor a Polynomial 1) Always begin by asking yourself, “Can I factor out a GCF?” If so, factor it out. 2) Look at the expression to decide whether it will factor further. Apply the appropriate method to factor. If there are a) two terms, see whether it is a difference of two squares, as in Section 7.4. b) three terms, see whether it can be factored using the methods of Section 7.2 or Section 7.3, or determine whether it is a perfect square trinomial (Section 7.4). c) four terms, see whether it can be factored by grouping as in Section 7.1. 3) After factoring, always look carefully at the result and ask yourself, “Can I factor it again?” If so, factor again. Look back in the chapter and make a list of the different types of factoring problems we have seen. Let’s learn how to decide which factoring method should be used to factor a particular polynomial. EXAMPLE 1 In-Class Example 1 Factor completely. a) 45m2 20n2 b) w2 10w 24 c) xy2 x 7y2 7 d) b2 8b 16 e) 8r2 14r 6 f) h2 49 Factor completely. a) 8x2 50y2 b) t2 t 56 c) a2b 9b 4a2 36 d) k2 12k 36 e) 15p2 51p 18 f ) c2 4 Solution a) “Can I factor out a GCF?” is the fi rst thing you should ask yourself. Yes. Factor out 2. 8x2 50y2 2(4x2 25y2) 420 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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