Practice Factoring in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Rewriting an algebraic expression as a product of two or more simpler expressions that multiply to give the original.

Reverse distribution: instead of expanding (x+2)(x+3)(x+2)(x+3), you compress x2+5x+6x^2 + 5x + 6 into the same product.

Showing a random 20 of 50 problems.

Example 1

easy
Factor: 4y2−254y^2 - 25.

Example 2

medium
Factor: x2+4x+4x^2 + 4x + 4.

Example 3

medium
Factor: 3x2−10x+33x^2 - 10x + 3.

Example 4

easy
Factor: x2−25x^2 - 25.

Example 5

medium
Factor: x3+2x2−x−2x^3 + 2x^2 - x - 2.

Example 6

hard
Factor: 6x2+x−26x^2 + x - 2.

Example 7

easy
Factor: x2+x−12x^2 + x - 12.

Example 8

medium
Factor: x2−8x+16x^2 - 8x + 16.

Example 9

hard
Factor: x2+4x+4−y2x^2 + 4x + 4 - y^2.

Example 10

medium
Factor: x2−4x−21x^2 - 4x - 21.

Example 11

medium
Factor completely: 3x2−273x^2 - 27.

Example 12

hard
Factor: x2+6xy+9y2x^2 + 6xy + 9y^2.

Example 13

medium
Factor: 2x2+7x+32x^2 + 7x + 3.

Example 14

medium
Solve x2−5x+6=0x^2 - 5x + 6 = 0 by factoring.

Example 15

easy
Factor: x2+8x+15x^2 + 8x + 15.

Example 16

hard
Factor: x2−12x+36x^2 - 12x + 36.

Example 17

easy
Factor: x2−10x+16x^2 - 10x + 16.

Example 18

medium
Factor: a3−8a^3 - 8.

Example 19

medium
Factor: 9−x29 - x^2.

Example 20

easy
Factor: 5x2−10x5x^2 - 10x.
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