What is Factorisation?

Factorisation is the process of expressing an algebraic expression as a product of two or more algebraic expressions. Factorisation is the reverse of expansion.

x2 + 5x+6 = x2 + 3x+ 2x+ 6
= x(x+ 3) + 2x+ 6                 (by factorising the first two terms)
= x(x+ 3) + 2(x+ 3)              (by factorising the last two terms)
= (x+ 3)(x+ 2)                     (by noting the common factor of x+ 3)

Example
Suppose we want to factorise the quadratic expression x2 −9x−22 by inspection.
We write
x2 −9x−22 = (      )(      )
and try to place the correct quantities in brackets. Clearly we will need an x in both terms:
x2 −9x−22 = (   x   )(   x  )
We want two numbers which multiply to give −22 and add to give −9. The two numbers are
−11 and +2.

x2 −9x−22 = (x−11)(x+ 2)