x^3-6x^2+11x-6

Question

Has to be answered in (x   )(x   ) form

Answer 1

Let f(x)=x³-6x²+11x-6.

Look for rational zeroes, so break 6 down into factors: 1, 2, 3, 6.

Set x to each of these (positive and negative) and test for zero until a zero is found (if any):

f(1)=1-6+11-6=0, so x=1 is a zero and x-1 is a factor. Use synthetic division to reduce to a quadratic:

1 | 1 -6 11  -6

     1  1 -5 | 6

     1 -5  6 | 0 = x²-5x+6=(x-2)(x-3).

So x³-6x²+11x-6=(x-1)(x-2)(x-3).