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Factoring (Math)

See how to factor a polynomial.
25 examples and their solutions.

How to Find the Factors of a Number

Example

Factors of 30
Solution

Example

Factors of 16
Solution

Prime Number

2, 3, 5, 7, 11, 13, 17, ...

A prime number is a number
that has only two factors:
1 and itself.
2, 3, 5, 7, 11, 13, 17, ...
are prime numbers.
1 has only one factor: 1.
So 1 is not a prime.

Prime Factorization

Example

Prime factorization of 60
Solution

Example

Prime factorization of 200
Solution

Greatest Common Factor

Example

GCF of 18 and 60
Solution

Example

GCF of 6a3c and 2a2bc2
Solution

Least Common Multiple

Example

LCM of 18 and 60
Solution

Example

LCM of 6a3c and 2a2bc2
Solution

Factoring: Common Monomial Factor

Example

x3 + 3x
Solution

Example

a2 - 2ab + 4a
Solution

Factoring by Grouping

Example

a2 - 2a + 5a - 10
Solution

Example

x2 - 4xy - 3x + 12y
Solution

Factoring a Quadratic Trinomial

Example

x2 + 3x + 2
Solution

Example

x2 - 5x + 6
Solution

Example

x2 - x - 12
Solution

Example

x2 + 5xy - 24y2
Solution

Example

2x2 + 7x + 6
Solution

Factoring a2 ± 2ab + b2

Formula

a2 ± 2ab + b2
= (a ± b)2

Example

x2 + 6x + 9
Solution

Example

x2 - 10x + 25
Solution

Factoring a2 - b2

Formula

a2 - b2
= (a + b)(a - b)

Example

x2 - 81
Solution

Example

16a2 - 49b2
Solution

Example

x4 - 1
Solution

Factoring a3 + b3

Formula

a3 + b3
= (a + b)(a2 - ab + b2)

Example

x3 + 8
Solution

Factoring a3 - b3

Formula

a3 - b3
= (a - b)(a2 + ab + b2)

Example

x3 - 125
Solution

Example

x6 - 1
Solution