Foundation and Higher · factorising
Factorising is
expanding
in reverse.
put the
brackets back
to factorise means —
Factorise
write it as a multiplication
using brackets
step 1 of 4
Take out a number
1. Biggest number going into both: 3.
2. Divide each term by 3 for the bracket.
✓ Expand to check: 6x + 15
6x + 15
3 × 2x + 3 × 5
= 3(2x + 5)
step 2 of 4
Take out a letter too
1. 2 goes into both 4 and 10.
2. Both terms have an x: take that out too.
✓ Nothing in common left inside
4x² + 10x
2x × 2x + 2x × 5
= 2x(2x + 5)
step 3 of 4
Quadratics: two brackets
1. Two numbers that multiply to make 10…
2. …and add to make 7. That is 2 and 5.
✓ 2 × 5 = 10 and 2 + 5 = 7
x² + 7x + 10
× to 10 + to 7
2 and 5
= (x + 2)(x + 5)
step 4 of 4
Difference of two squares
1. A square take away a square.
2. Same brackets: one +, one −.
✓ The middle terms cancel out
x² − 9
x² − 3²
= (x + 3)(x − 3)
factorising —
One bracket
take out the biggest factor
Two brackets
× to the end, + to the middle
Always expand your answer
to check it.
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