Practice Factoring Out the GCF in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Factoring out the greatest common factor (GCF) means identifying the largest expression that divides every term, then rewriting the polynomial as that GCF times what remains.

Look at what all terms share in common—like taking the common ingredient out of a recipe. In 6x3+9x26x^3 + 9x^2, every term has at least 3x23x^2 in it, so pull it out front: 3x2(2x+3)3x^2(2x + 3).

Showing a random 20 of 50 problems.

Example 1

easy
Factor out the GCF: 6x+96x+9.

Example 2

easy
Factor out the GCF: 7x2−77x^2-7.

Example 3

easy
Factor out the GCF: 8x+128x + 12.

Example 4

easy
Factor out the GCF: 3x2+9x3x^2+9x.

Example 5

hard
Factor: 3xn+2+6xn+1−9xn3x^{n+2} + 6x^{n+1} - 9x^n for integer n≥0n \geq 0.

Example 6

easy
Factor out the GCF: x2+xx^2+x.

Example 7

hard
Factor by grouping: 2x3−6x2+5x−152x^3 - 6x^2 + 5x - 15.

Example 8

medium
What is the GCF of 18x3y218x^3y^2, 24x2y324x^2y^3, and 12xy212xy^2?

Example 9

medium
Factor: x(x+2)+3(x+2)x(x+2)+3(x+2) by taking out the common binomial.

Example 10

easy
Factor out the GCF: 5x3+10x25x^3+10x^2.

Example 11

challenge
Factor completely: 6x4−6x26x^4-6x^2.

Example 12

challenge
For what value of kk is 3x3x the GCF of 6x2+kx6x^2+kx? Find kk and the factored form.

Example 13

challenge
Factor out the GCF including a binomial power: 4(x+1)3−8(x+1)24(x+1)^3-8(x+1)^2.

Example 14

medium
A box has volume 4x3+8x24x^3+8x^2. Factor to express it as height times base area, where height is the GCF's variable part.

Example 15

easy
Factor out the GCF: 4x2+8x4x^2+8x.

Example 16

medium
Factor: x(x+2)+3(x+2)x(x + 2) + 3(x + 2).

Example 17

medium
Factor out the GCF: 14x4+21x3−7x214x^4+21x^3-7x^2.

Example 18

medium
Factor: 20a3b2−30a2b3+50ab20a^3b^2 - 30a^2b^3 + 50ab.

Example 19

easy
Factor: x3+x2x^3 + x^2.

Example 20

challenge
Factor completely: 6x4−24x26x^4 - 24x^2.
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