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. Write the procedure in your own words. EXAMPLE 9 In-Class Example 9 Factor 4c5 28c4 8c3 56c2 completely. Answer: 4c2(c 7)(c2 2) Factor 7h4 7h3 42h2 42h completely. 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 7h. 7h4 7h3 42h2 42h 7h(h3 h2 6h 6) Factor out the GCF, 7h. The polynomial in parentheses has four terms. Try to factor it by grouping. 7h(h3 h2 6h 6) 7hh2(h 1) 6(h 1) Take out the common factor in each group. 7h(h 1)(h2 6) Factor out (h 1) using the distributive property. c Check by multiplying: 7h(h 1)(h2 6) 7h(h3 h2 6h 6) 7h4 7h3 42h2 42h ✓ YOU TRY 8 Factor 12t3 12t2 3t2u 3tu completely. 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) y5 2) a) 9w5 b) 2hk2 c) 6c2 3) a) 2(w 8) b) 3u4(u2 12u 5) c) z2(z3 9) d) 9r2t(5r2t2 4r2t 2rt 1) 4) y2(y2 10y 8) 5) a) (d 8)(c 2) b) (k2 15)(k 7) c) (v 2)(u 1) 6) a) (y 4)(x 10) b) (5p 8q)(r 2) c) (w 9)(w2 6) 7) (3k 8)(k 6m) 8) 3t(t 1)(4t u) www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 395
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above