Factoring Polynomials 125
Step 3. Use the distributive property to factor −2 from the resulting
expression.
=− 2 (x^3 − 2 x+ 4)
Step 4. Review the main steps.
−− 24 xx^3 +++ 44 8282 =− (()− +
A Quantity as a Common Factor
You might have a common quantity as a factor in the GCF.
Problem Factor.
a. x(x− 1) + 2(x− 1)
b. a(c+d) + (c+d)
c. 2 x(x− 3) + 5(3 −x)
Solution
a. x(x− 1) + 2(x− 1)
Step 1. Determine the GCF for x(x− 1) and 2(x− 1).
GCF = (x− 1)
Step 2. Use the distributive property to factor (x − 1) from the expression.
x()x− )+ (^2) ()xx−
=()− ()+
b. a(c + d) + (c + d)
Step 1. Determine the GCF for a(c + d) and (c + d).
GCF = (c + d)
Step 2. Use the distributive property to factor (c+d) from the expression.
ac( +dc) (c+d)
=+ac(( dc))+ (((c+ddd))))=(((( ))))((()( +
Think
+
c. 2 x(x − 3) + 5(3 − x)
Step 1. Because (3 − x) = −1(x − 3), factor −1 from the second term.
a(c + d) + (c + d) ≠ (c + d)a. Don’t leave
off the 1. Think of (c + d) as 1(c + d).