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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

Factors of 30
Solution

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

GCF of 18 and 60
Solution

### Example

GCF of 6a3c and 2a2bc2
Solution

## Least Common Multiple

LCM of 18 and 60
Solution

### Example

LCM of 6a3c and 2a2bc2
Solution

x3 + 3x
Solution

a2 - 2ab + 4a
Solution

## Factoring by Grouping

### Example

a2 - 2a + 5a - 10
Solution

### Example

x2 - 4xy - 3x + 12y
Solution

x2 + 3x + 2
Solution

x2 - 5x + 6
Solution

x2 - x - 12
Solution

x2 + 5xy - 24y2
Solution

2x2 + 7x + 6
Solution

a2 ± 2ab + b2
= (a ± b)2

x2 + 6x + 9
Solution

x2 - 10x + 25
Solution

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

x2 - 81
Solution

16a2 - 49b2
Solution

x4 - 1
Solution

## Factoring a3 + b3

### Formula

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

x3 + 8
Solution

## Factoring a3 - b3

### Formula

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

x3 - 125
Solution

x6 - 1
Solution