← Algebra I

Algebra I

Factoring

Lesson

Factoring is the reverse of multiplying. Given a polynomial, find what was multiplied to produce it.

Method 1: Greatest Common Factor (GCF)

Pull out the largest factor that divides every term.

6x2+9x=3x(2x+3)6x^2 + 9x = 3x(2x + 3)

Both terms share a factor of 3x3x.

Method 2: Trinomial of the form x2+bx+cx^2 + bx + c

Find two numbers that multiply to c and add to b. Those numbers go in the factored form (x+p)(x+q)(x + p)(x + q).

x2+7x+10x^2 + 7x + 10

Find two numbers that multiply to 10 and add to 7. Those are 2 and 5.

x2+7x+10=(x+2)(x+5)x^2 + 7x + 10 = (x + 2)(x + 5)

Method 3: Difference of squares

a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)
x2−25=(x+5)(x−5)x^2 - 25 = (x + 5)(x - 5)

How to type your answer

For trinomials and differences of squares, write factors with the smaller constant first (e.g. (x+2)(x+5), not (x+5)(x+2)). For differences of squares, the plus factor comes first (e.g. (x+5)(x-5)). For GCF: write the factor outside, then the parentheses (e.g. 3x(2x+3)). No spaces.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

2x+62x + 6

Problem 2

3x+123x + 12

Problem 3

x2+3x+2x^2 + 3x + 2

Problem 4

x2−4x^2 - 4

Practice

Standard problems matching the lesson.

Problem 5

5x+155x + 15

Problem 6

6x2+9x6x^2 + 9x

Problem 7

4x2−8x4x^2 - 8x

Problem 8

A rectangle has area x^2 + 7x + 10. Factor to find its dimensions.

Problem 9

A rectangle has area x^2 + 8x + 12. Factor to find its dimensions.

Problem 10

A rectangle has area x^2 + 6x + 8. Factor to find its dimensions.

Problem 11

A rectangle has area x^2 - 5x + 6. Factor to find its dimensions.

Problem 12

A rectangle has area x^2 - 9x + 20. Factor to find its dimensions.

Problem 13

A rectangle has area x^2 + x - 12. Factor to find its dimensions.

Problem 14

A rectangle has area x^2 - 2x - 15. Factor to find its dimensions.

Problem 15

x2−25x^2 - 25

Problem 16

x2−49x^2 - 49

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

x2−100x^2 - 100

Problem 18

A square garden has area x^2 + 10x + 25. Factor to find its side.

Problem 19

A square garden has area x^2 - 12x + 36. Factor to find its side.

Problem 20

A rectangle has area x^2 + 2x - 24. Factor to find its dimensions.

Problem 21

10x2−25x10x^2 - 25x

Problem 22

A rectangle has area x^2 - 11x + 28. Factor to find its dimensions.

Practice

Standard problems matching the lesson.

Problem 23

A rectangle has area x^2 + 7x + 10 square units. Write its dimensions as a product of two binomials.

Problem 24

A square plot loses a small square cutout, leaving area x^2 - 25. Write this as a product of two binomials.

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 25

A garden plot has area x^2 - 11x + 28 square feet. Factor to express its dimensions.

Ask the tutor

Stuck on a concept? Want another example? Ask anything about this topic.

Type your own question below, or tap one of the suggestions. The tutor can re-explain the lesson, work through a specific problem with you, generate fresh practice tuned to where you are, or check your reasoning.

Quiz

Test yourself on this topic →

10 questions, no hints. About 5 minutes.