Easy Algebra Step-by-Step

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).