The GCF of x( y 2) and 9( y 2) is ( y 2). Use the distributive property to factor out y 2. x( y 2) 9( y 2) ( y 2)(x 9) Distributive property Check: ( y 2)(x 9) ( y 2)x ( y 2)9 Distribute. The result (y 2)x (y 2)9 is the same as x(y 2) 9(y 2) because multiplication is commutative. ✓ b) Let’s begin by rewriting r(s 4) (s 4) as r(s 4) 1(s 4). term term The GCF is s 4. r(s 4) 1(s 4) (s 4)(r 1) Distributive property The check is left to the student. It is important to write 1 in front of (s 4). Otherwise, the following mistake is often made: r (s 4) (s 4) (s 4)r THIS IS INCORRECT! The correct factor is r 1 not r. The GCF can also be a binomial. Notice how the distributive property is being used in this case. Always write a “1” in front of the parentheses in a problem like Example 6b). YOU TRY 5 Factor out the GCF. a) t(u 8) 5(u 8) b) z(z2 2) 6(z2 2) c) 2n(m 7) (m 7) Taking out a binomial factor leads us to our next method of factoring—factoring by grouping. 5 Factor by Grouping When we are asked to factor a polynomial containing four terms, we often try to factor by grouping. EXAMPLE 7 Factor by grouping. a) ab 5a 3b 15 b) 2pr 5qr 6p 15q c) x3 6x2 7x 42 www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 361
messersmith_power_intermediate_algebra_1e_ch4_7_10
To see the actual publication please follow the link above