Easy Algebra Step-by-Step

Factoring Polynomials 123

Step 4. Review the main steps.

xy^3 −+xyxy yyy()xxx^3 + 1

d. 4 x+ 4 y

Step 1.Use the distributive property to factor 4 from the polynomial.

44 xy 4

= (^4) ()++

GCF with a Negative Coeffi cient

At times, you might need to factor out a GCF that

has a negative coeffi cient. To avoid sign errors,

mentally change subtraction to add the opposite.

Problem Factor using a negative coeffi cient for the GCF.

a. − 5 xy^2 + 10 xy

b. − 5 xy^2 − 10 xy

c. −x − y

d. − 2 x^3 + 4 x − 8

Solution

a. − 5 xy^2 + 10 xy

Step 1. Determine the GCF with a negative coeffi cient for − 5 xy^2 and 10xy.

GCF = − 5 xy

Step 2. Rewrite each term of the polynomial as an equivalent product of

− 5 xy and a second factor.

− 51 xy^2 + 0 xy

=− 55 xy⋅−y xy⋅− 2

Step 3. Use the distributive property to factor

− 5 xy from the resulting expression.

=− 5 xy(y− 2)

Step 4. Review the main steps.

− 51 xy^2 + 05 xy=− xy()−

When factoring out a GCF that

has a negative coeffi cient, always

mentally multiply the factors and

check the signs.

− 5 xy^2 + 10 xy ≠ − 5 xy ⋅ y − 5 xy ⋅ 2.

Check the signs!

x^3 y − xy + y ≠ y(x^3 − x). Don’t

forget the 1.