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Unit F3 Section 3
Linear Factorisation
The process of removing brackets is known as expanding. The reverse process is known as factorisation, where an expression is rewritten as a product of terms.
To factorise an expression it is necessary to identify numbers or variables which are factors common to all the terms.
Worked Examples
1
Factorise 6x + 8.
Both terms (6x) and (8) can be divided by 2, so the expression is factorised as
| 6x + 8 | = (2 × 3x) + (2 × 4) |
| = 2(3x + 4) |
2
Factorise 12a − 16.
Here the largest number by which both terms, (12a) and (16), can be divided is 4.
| 12a − 16 | = (4 × 3a) − (4 × 4) |
| = 4(3a − 4) |
3
Factorise 4x2 − 8x .
Here 4 is the largest number that will divide both terms, but each term can also be divided by x, so 4x is the factor common to both terms.
| 4x2 − 8x | = (4x × x) − (4x × 2) |
| = 4x(x − 2) |
Exercises
