Answer:
[tex]f(x) =(x-1)(x-2)(x-3)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^3-6x^2+11x-6[/tex]
Required
The factored form
[tex]f(x) = x^3-6x^2+11x-6[/tex]
Split
[tex]f(x) =x^3 -3x^2- 3x^2 +2x +9x -6[/tex]
Rearrange as:
[tex]f(x) = x^3 -3x^2 +2x - 3x^2+9x -6[/tex]
Factorize
[tex]f(x) = x(x^2 - 3x + 2) - 3(x^2 - 3x + 2)[/tex]
Factor out [tex]x^2 - 3x + 2[/tex]
[tex]f(x) = (x^2 - 3x + 2)(x - 3)[/tex]
Expand
[tex]f(x) = (x^2 - 2x - x + 2)(x - 3)[/tex]
Factorize
[tex]f(x) = (x(x - 2) - 1(x - 2))(x - 3)[/tex]
Factor out [tex]x - 2[/tex]
[tex]f(x) = (x - 1) (x - 2)(x - 3)[/tex]
