Sometimes we need to take out a negative factor. EXAMPLE 5 In-Class Example 5 Factor out 3w from 27w3 12w2 6w. Answer: 3w(9w2 4w 2) Factor out 2k from 6k4 10k3 8k2 2k. Solution 6k4 10k3 8k2 2k (2k)(3k3) (2k)(5k2) (2k)(4k) (2k)(1) 2k3k3 (5k2) 4k (1) 2k(3k3 5k2 4k 1) Rewrite using 2k as one of the factors. Distributive property Rewrite (5k2) as 5k2 and (1) as 1. Check: 2k(3k3 5k2 4k 1) 6k4 10k3 8k2 2k ✓ When taking out a negative factor, be very careful with the signs! YOU TRY 4 Factor out y2 from y4 10y3 8y2. 3 Factor Out the Greatest Common Binomial Factor Until now, all of the GCFs have been monomials. Sometimes, however, the greatest common factor is a binomial. EXAMPLE 6 In-Class Example 6 Factor out the GCF. a) p(q 4) 10(q 4) b) m(n 8) (n 8) Answer: a) (q 4)(p 10) b) (n 8)(m 1) Factor out the greatest common factor. a) a(b 5) 8(b 5) b) x(y 3) (y 3) Solution a) In the polynomial a(b 5) 8(b 5), a(b 5) is a term and 8(b 5) is a term. term term c c What do these terms have in common? b 5 The GCF of a(b 5) and 8(b 5) is b 5. Use the distributive property to factor out b 5. a(b 5) 8(b 5) (b 5)(a 8) Distributive property Check: (b 5)(a 8) (b 5)a (b 5)8 Distribute. a(b 5) 8(b 5) Commutative property b) Begin by writing x(y 3) (y 3) as x(y 3) 1(y 3). The GCF is y 3. x(y 3) 1(y 3) (y 3)(x 1) Distributive property The check is left to the student. 392 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