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.