Practice Factoring Intuition 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

Understanding factoring as finding what multiplies together to give an expression.

Reverse engineering multiplication: 'What times what gives x2+5x+6x^2 + 5x + 6?'

Showing a random 20 of 50 problems.

Example 1

medium
Factor x2+2x−8x^2+2x-8.

Example 2

easy
Factor x2−16x^2-16.

Example 3

hard
Factor x4−16x^4-16 completely.

Example 4

hard
Factor x2+10xy+25y2x^2+10xy+25y^2.

Example 5

easy
Two numbers multiply to −12-12 and add to 11. Find them.

Example 6

medium
What two numbers multiply to 3030 and add to −11-11?

Example 7

easy
Find two numbers that multiply to 18 and add to 9.

Example 8

medium
Factor 4x2−94x^2-9.

Example 9

medium
Factor 2x2+10x+122x^2+10x+12 completely.

Example 10

challenge
Factor x4−16x^4-16 completely over the reals.

Example 11

hard
Factor 6x2+11x−106x^2+11x-10.

Example 12

medium
Factor x2−10x+25x^2-10x+25.

Example 13

hard
Factor 3x2−10x−83x^2-10x-8.

Example 14

challenge
Use factoring to simplify x2−x−6x2−9\frac{x^2-x-6}{x^2-9} (state restrictions).

Example 15

easy
Factor out the greatest common factor of 6x+96x+9.

Example 16

easy
Factor x2−1x^2-1.

Example 17

medium
Factor x3−xx^3-x completely.

Example 18

challenge
Factor x2+(a+b)x+abx^2+(a+b)x+ab symbolically.

Example 19

easy
Factor x2+2x−15x^2+2x-15.

Example 20

easy
Factor x2−5x+6x^2-5x+6.
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