Brackets & Factors

OCR Stage 6

What is 3(2 + 4) ?

3 ‘lots’ of ‘2 + 4’ = 3 ‘lots’ of 6 = 18

2 4

3

x

6 12 = 18

What is 3(x + 4) ?

x 4

3

x

3x 12 = 3x + 12

3 ‘lots’ of ‘x + 4’

What is 5(2x + 1) ?

2x 1

5

x

10x 5 = 10x + 5

5 ‘lots’ of ‘2x + 1’

What is 4(x - 2) ?

x -2

4

x

4x -8 = 4x - 8

4 ‘lots’ of ‘x - 2’

What is x(x + 3) ?

x 3

x

x

x2 3x = x2 + 3x

x ‘lots’ of ‘x + 3’

What is x times x?

What is 2x(x - 3) ?

x -3

2x

x

2x2 -6x = 2x2 – 6x

2x ‘lots’ of ‘x - 3’

What is -x(2x + 3) ?

2x 3

-x

x

-2x2 -3x = -2x2 – 3x

-x ‘lots’ of ‘2x + 3’

We call this process ‘expanding a bracket’

Factorising an expression

• This is the reverse of expanding a bracket

Eg Factorise 4x + 2

What is a Factor? A FACTOR of a number is a number that divides into the number EXACTLY

Eg Factorise 4x + 2What number divides

into BOTH parts of the expression

EXACTLY?

2 4x + 2

2x +1

= 2(2x + 1)

How could we check this?

Eg Factorise 6x - 9What number divides

into BOTH parts of the expression

EXACTLY?

3 6x - 9

2x - 3

= 3(2x – 3)

Eg Factorise x2 + xWhat number divides

into BOTH parts of the expression

EXACTLY?

x x2 + x

x + 1

= x(x + 1)

Eg Factorise 8x2 – 4xWhat number divides

into BOTH parts of the expression

EXACTLY?

4x 8x2 – 4x

2x - 1

= 4x(2x - 1)

Eg Factorise 6 - 4x2

What number divides into BOTH parts of

the expression EXACTLY?

2 6 - 4x2

3 - 2x2

= 2(3 – 2x2)