You will not always factor correctly on the first try. Don’t worry, just try again! EXAMPLE 4 In-Class Example 4 Factor 2m2 13m 20 completely. Answer: (2m 5)(m 4) Begin with the squared term, 2x2. Which two expressions with integer coeffi cients can we multiply to get 2x2? 2x and x. Put these in the binomials. 2x2 11x 15 (2x )(x ) 2x x 2x2 Next, look at the last term, 15. What are the pairs of positive integers that multiply to 15? They are 15 and 1 as well as 5 and 3. Try these numbers as the last terms of the binomials. The middle term, 11x, comes from fi nding the sum of the products of the outer terms and inner terms. First Try 2x2 11x 15 (2x 15)(x 1) Incorrect! 15x 2x 17x These must both be 11x. Try again. Switch the 15 and the 1. 2x2 11x 15 (2x 1)(x 15) Incorrect! 1x 30x 31x These must both be 11x. Try using 5 and 3. 2x2 11x 15 (2x 5)(x 3) Correct! 5x 6x 11x These must both be 11x. Therefore, 2x2 11x 15 (2x 5)(x 3). Check by multiplying. Factor 3t2 29t 18 completely. Solution Can we factor out a GCF? No. To get a product of 3t2, we will use 3t and t. 3t2 29t 18 (3t )(t ) 3t t 3t2 Since the last term is positive and the middle term is negative, we want pairs of negative integers that multiply to 18. The pairs are 1 and 18, 2 and 9, and 3 and 6. Try these numbers as the last terms of the binomials. The middle term, 29t, comes from fi nding the sum of the products of the outer terms and inner terms. 3t2 29t 18 (3t 1)(t 18) Incorrect! t (54t) 55t These must both be 29t. Try again. Switch the 1 and the 18: 3t 2 29t 18 (3t 18)(t 1) Without multiplying, we know that this choice is incorrect. How? In the factor (3t 18), a 3 can be factored out to get 3(t 6). But, we concluded that we could not factor out a GCF from the original polynomial, 3t 2 29t 18. Therefore, it will not be possible to take out a common factor from one of the binomial factors. Note If you cannot factor out a GCF from the original polynomial, then you cannot take out a factor from one of the binomial factors either. 408 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above