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messersmith_power_introductory_algebra_1e_ch4_7_10

It is important to write 1 in front of (y 3). Otherwise, the following mistake is often made: x(y 3) (y 3) (y 3)x This is incorrect! The correct factor is x 1, not x. YOU TRY 5 Factor out the GCF. a) c(d 8) 2(d 8) b) k(k2 15) 7(k2 15) c) u(v 2) (v 2) Taking out a binomial factor leads us to our next method of factoring—factoring by grouping. 4 Factor by Grouping When we are asked to factor a polynomial containing four terms, we often try to factor by grouping. EXAMPLE 7 In-Class Example 7 Factor by grouping. a) ac 9a 5c 45 b) 2mp 5np 8m 20n c) x3 8x2 7x 56 Answer: a) (c 9)(a 5) b) (2m 5n)(p 4) c) (x 8)(x2 7) Factor by grouping. a) rt 7r 2t 14 b) 3xz 4yz 18x 24y c) n3 8n2 5n 40 Solution a) Begin by grouping terms together so that each group has a common factor. rt 7r 2t 14 c c T T Factor out r to get r(t 7). r(t 7) 2(t 7) Factor out 2 to get 2(t 7). (t 7)(r 2) Factor out (t 7). Check by multiplying: (t 7)(r 2) rt 7r 2t 14 ✓ b) Group terms together so that each group has a common factor. 3xz 4yz 18x 24y d d T T Factor out z to get z(3x 4y). z(3x 4y) 6(3x 4y) Factor out 6 to get 6(3x 4y). (3x 4y)(z 6) Factor out (3x 4y). Check by multiplying: (3x 4y)(z 6) 3xz 4yz 18x 24 ✓ c) Group terms together so that each group has a common factor. n3 8n2 5n 40 T T d d Factor out n2 to get n2(n 8). n2(n 8) 5(n 8) Factor out 5 to get 5(n 8). (n 8)(n2 5) Factor out (n 8). Complete each example, and notice the new steps compared with those in the example before it. www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 393


messersmith_power_introductory_algebra_1e_ch4_7_10
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