Factorise the expression x3−6x2+11x−6.
By factor theorem, (x+1) is a factor of x3−6x2+11x−6.
Performing long division as shown below:
x2−5x+6x−1)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x3−6x2+11x−6 x3−x2 − + ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ −5x2+11x−6 −5x2+5x + − ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 6x−6 6x−6 ––––––––––––– 0 –––––––––––––