Factoring a Polynomial by Finding the GCF
Factor: -6x4y2 - 30x2y3 - 2x2y
|Step 1 Identify the terms of the polynomial.
Step 2 Factor each term.
|-6x4y2, - 30x2y3, - 2x2y
|Each term has a negative
coefficient. So, we include -1 as a factor of each term.
|= -1 Â· 2 Â· 3 Â· x
Â· x Â· x Â· x Â· y Â· y
= -1 Â· 2 Â· 3 Â· 5
Â· x Â· x Â· y Â· y Â· y
= -1 Â· 2 Â· x Â· x Â· y
|Step 3 Find the GCF of the terms.
In the lists, the common factors are -1, 2, x, x, and y.
So, a common factor of each term is:
-1 Â· 2 Â· x
Â· x Â· y
|Step 4 Rewrite each term using the GCF.
To avoid an error with the signs, write each subtraction as an addition of
||-6x4y2 - 30x2y3 - 2x2y
= -6x4y2 + (-30x2y3) + (-2x2y)
|Rewrite each term
using -2x2y as a
||= -2x2y Â· 3x2y
+ (-2x2y) Â· 15y2
+ (-2x2y) Â· 1
|Step 5 Factor out the GCF.
Factor out -2x2y.
= -2x2y(3x2y + 15y2
Thus, -6x4y2 - 30x2y3 - 2x2y
= -2x2y(3x2y + 15y2 + 1).
You can multiply to check the factorization. We leave the check to you.
Note that the third term, -2x2y, is the common factor.
So we write that term as -2x2y Â· 1.
We can also factor the polynomial
using +2x2y as the common factor.
Then we have:
||= 30x2y3 - 2x2y
= 2x2y(-3x2y - 15y2 - 1)