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Factoring a Polynomial by Finding the GCF
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Properties of Exponents
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Multiplication Property of Equality
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Multiplying and Dividing Fractions 1
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
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Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
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Equations 1
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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 · 2 · 3 · x · x · x · x · y · y

= -1 · 2 · 3 · 5 · x · x · y · y · y

= -1 · 2 · x · x · 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 · 2 · x · x · 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 · 3x2y + (-2x2y) · 15y2 + (-2x2y) · 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 · 1.

We can also factor the polynomial using +2x2y as the common factor.

Then we have:

-6x4y2 = 30x2y3 - 2x2y

= 2x2y(-3x2y - 15y2 - 1)

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