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• Subject: Mathematics
• AS: 91261
• Level: 2
• Credits: 4
• External

## Mathematics 2.6 Apply algebraic methods in solving problems

### Factorising algebraic expressions

Factorise is the reverse of expand i.e. put in brackets.

To factorise, rewrite the expression as factors multiplied together.

#### Two terms

Look for the largest number that will divide into all terms and any common letters.

``` e.g.   12x + 20xy = 4x(3 + 5y)
This is because 4x is the largest factor of both 12x and
20xy.
```

See online examples of common factors.

#### Two terms: Difference of two squares

Look for two square terms that have been subtracted.

``` e.g.   4x2 – 9
= (2x)2 – 32
= (2x + 3)(2x – 3)
```

See online examples of factoring the difference of squares.

#### Three terms

Look for a common factor first and then factorise further.

``` e.g.   3x2 – 6x – 15 = 3(x2 – 2x – 5)
```

If no common factor, look for two numbers that multiply to give the number by itself (constant term) and add to give the number in front of x.

``` e.g.   x2 – 2x - 15 = (x + 3)(x – 5)
This is because –5 times 3 = –15 and –5 plus 3 = –2
```

Check

``` Hence   3x2 – 6x – 45 = 3(x + 3)(x – 5)
```

If there is no number written in front of x remember it is really a 1.

``` e.g.   x2 + x – 6 = (x + 3)(x – 2)
This is because 3 times -2 = –6 and 3 plus –2 = 1
```

See notes on:

#### Harder factorising

If there is a number in front of x2 that is not a common factor use guess and check or the following method.

Two numbers that multiply to give –6 and add to give +5 are +6 and –1. Write 5x as 6x - x.

``` e.g.   2x2 + 5x – 3= 2x2 + 6x – x – 3
```

When there are four terms, factorise in pairs first.

``` e.g.   2x2 + 6x – x – 3 = 2x(x + 3) – 1(x + 3)
```

Take out the common bracket (x + 3).

``` e.g.   2x(x + 3) – 1(x + 3) = (x + 3)(2x – 1)
```

See notes on:

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