For 10x² + x − 3, multiply a and c: 10 × −3 = −30. Find two numbers that multiply to −30 and add to b = 1: 6 and −5. Split the middle term: 10x² + 6x − 5x − 3.
Now factorise in pairs: 2x(5x + 3) − 1(5x + 3) = (2x − 1)(5x + 3). Always take out a common factor first: 2x² − 6x − 8 = 2(x² − 3x − 4) = 2(x − 4)(x + 1).
Worked example
Factorise fully 6x² + 7x + 2
- ac = 12; numbers 3 and 4 add to 7.
- 6x² + 3x + 4x + 2 = 3x(2x + 1) + 2(2x + 1).
Answer:(3x + 2)(2x + 1)
Key words
- leading coefficient
- the number in front of x²
- split the middle term
- rewrite bx as two terms
- factorise fully
- no common factor left
Practise this
New questions every time.
Common Core-referenced: HSA-SSE.A.2