Factorising
Factorising
- You can write expressions as a product of their factors
- Factorising is the opposite of expanding brackets
Quadratics
Factorising a Quadratic
- Find two factors of \(ac\) that add up to \(b\)
- Rewrite the b term as a sum of these two factors
- Factorise each pair of terms
- Take out the common factor
Example
- \(2x^2+5x-3\)
- \(2\) x \(-3 = -6\)
- 6 and -1 are factors of ac and add to b
- We can rewrite this as \((2x-1)(x+3)\) because 2x times by 3 makes 6x
\(25x-9x^3\)
- Take out x as a factor: \(x(25-9x^2)\)
- Factorise the quadratic using DOTS: \(x(5+3x)(5-3x)\)
- Fully factorised.