Ximpledu

# Factoring

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

• N = ab
a, b: factors of N
• Prime Factorization:
12 = 223
• a2bc = a2bc
ac2 = ac2
(GCF) = ac
• a2bc = a2bc
ac2 = ac2
(LCM) = a2bc2
• ax + ay + az
= a(x + y + z)
• ax + ay + bx + by
= a(x + y) + b(x + y)
= (a + b)(x + y)
• x2 + bx + c

mn = +c
m + n = +b

= (x + m)(x + n)
• a2 ± 2ab + b2
= (a ± b)2
• a2 - b2
= (a + b)(a - b)
• a3 + b3
= (a + b)(a2 - ab + b2)
• a3 - b3
= (a - b)(a2 + ab + b2)

## 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
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