YOU TRY 7 Factor 6a2 5b 15a 2ab completely. Often, we have to combine the two factoring techniques we have learned here. That is, we begin by factoring out the GCF and then we factor by grouping. Let’s summarize how to factor a polynomial by grouping, and then look at another example. Procedure Steps for Factoring by Grouping 1) Before trying to factor by grouping, look at each term in the polynomial and ask yourself, “Can I factor out a GCF fi rst?” If so, factor out the GCF from all of the terms. 2) Make two groups of two terms so that each group has a common factor. 3) Take out the common factor in each group of terms. 4) Factor out the common binomial factor using the distributive property. 5) Check the answer by multiplying the factors. EXAMPLE 9 Factor completely. 4y4 4y3 20y2 20y Solution Notice that this polynomial has four terms. This is a clue for us to try factoring by grouping. However, look at the polynomial carefully and ask yourself, “Can I factor out a GCF?” Yes! Therefore, the fi rst step in factoring this polynomial is to factor out 4y. 4y4 4y3 20y2 20y 4y(y3 y2 5y 5) Factor out the GCF, 4y. The polynomial in parentheses has 4 terms. Try to factor it by grouping. 4y(y3 y2 5y 5) 4yy2(y 1) 5(y 1) Take out the common factor in each group. 4y(y 1)(y2 5) Factor out ( y 1) using the distributive property. Check: 4y(y 1)(y2 5) 4y(y3 y2 5y 5) 4y4 4y3 20y2 20y ✓ Seeing a polynomial with 4 terms is your hint to try factoring by grouping. YOU TRY 8 Factor completely. 4ab 14b 8a 28 Remember, seeing a polynomial with four terms is a clue to try factoring by grouping. Not all polynomials will factor this way, however. We will learn other techniques later, and some polynomials must be factored using methods learned in later courses. ANSWERS TO YOU TRY EXERCISES 1) y4 2) a) 8p5 b) r4s3 3) a) 8k2(7k2 3k 5) b) 3a2b3(a2b 4ab 6b 1) 4) p2(p3 7p2 3p 11) 5) a) (u 8)(t 5) b) (z2 2)(z 6) c) (m 7)(2n 1) 6) a) (c 2)(2d 5) b) (k 9)(4k m) c) (h 8)(h2 5) 7) (2a 5)(3a b) 8) 2(b 2)(2a 7) www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 363
messersmith_power_intermediate_algebra_1e_ch4_7_10
To see the actual publication please follow the link above