Factorising is expanding backwards. To factorise x² + bx + c, find two numbers that multiply to c and add to b. For x² + 2x − 48, the numbers are 8 and −6, because 8 × −6 = −48 and 8 + (−6) = 2. So x² + 2x − 48 = (x + 8)(x − 6).
Look for special cases. x² − 16 is a difference of two squares: (x + 4)(x − 4). And always take out a common factor first: 3x² − 12 = 3(x² − 4) = 3(x + 2)(x − 2).
Worked example
Factorise x² − 9x + 14
- Find two numbers that multiply to 14 and add to −9.
- −7 and −2 work.
Answer:(x − 7)(x − 2)
Key words
- factorise
- write as a product of brackets
- quadratic
- an expression with x² as the highest power
- common factor
- a factor of every term
Practise this
New questions every time.
Common Core-referenced: HSA-SSE.A.2