Question

What is the factored from of the polynomial function f(x)=x3-6x2+11x-6

Answer 1

`f(x) =(x-1)(x-2)(x-3)`

Explanation:

Given

`f(x) = x^3-6x^2+11x-6`

Required

The factored form

`f(x) = x^3-6x^2+11x-6`

Split

`f(x) =x^3 -3x^2- 3x^2 +2x +9x -6`

Rearrange as:

`f(x) = x^3 -3x^2 +2x - 3x^2+9x -6`

Factorize

`f(x) = x(x^2 - 3x + 2) - 3(x^2 - 3x + 2)`

Factor out
`x^2 - 3x + 2`

`f(x) = (x^2 - 3x + 2)(x - 3)`

Expand

`f(x) = (x^2 - 2x - x + 2)(x - 3)`

Factorize

`f(x) = (x(x - 2) - 1(x - 2))(x - 3)`

Factor out
`x - 2`

`f(x) = (x - 1) (x - 2)(x - 3)`