Question

factorise x3-6x2+11x-6

Answer 1

f(x) = x3 - 6x2 + 11x - 6
Given that f(1) = 0
factorise f(x) completely

(x3 - 6x2 + 11x - 6)
divided by
(x - 1)
gives
(x2 - 5x + 6)

This quadratic expression
(x2 - 5x + 6)
will now factorise as
(x - 2)(x - 3)

Thus the full factorisation of f(x) is
(x - 1)(x - 2)(x - 3)