Easy Algebra Step-by-Step

(Marvins-Underground-K-12) #1
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.
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