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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Factoring a Polynomial by Finding the GCF

Example

Factor: -6x4y2 - 30x2y3 - 2x2y

Solution

 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. -6x4y2 -30x2y3 -2x2y = -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 = -2x2y Step 4 Rewrite each term using the GCF. To avoid an error with the signs, write each subtraction as an addition of the opposite. -6x4y2 - 30x2y3 - 2x2y = -6x4y2 + (-30x2y3) + (-2x2y) Rewrite each term using -2x2y as a factor. = -2x2y Â· 3x2y + (-2x2y) Â· 15y2 + (-2x2y) Â· 1 Step 5 Factor out the GCF. Factor out -2x2y. = -2x2y(3x2y + 15y2 + 1)

Thus, -6x4y2 - 30x2y3 - 2x2y  = -2x2y(3x2y + 15y2 + 1).

You can multiply to check the factorization. We leave the check to you.

Note:

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:

 -6x4y2 = 30x2y3 - 2x2y = 2x2y(-3x2y - 15y2 - 1)