Question

How to determine if (𝒙−𝟏) is a factor of $x^3-6x^2+11x-6?$

Answer 1

Given:
$f\left(x\right)=x^3-6x^2+11x-6$ and $g\left(x\right)=x-1$
$g\left(x\right)=x=1$
We have to find the remainder when f(x)is divided by g(x).
By applying remainder theorem, when f(x)is divided by g(x) we get,

Step 1:
f(1)= (1)3-6(1)2+11(1)-6.

Step 2:
f(1)=1-6+11-6
=12-12
= 0.
Hence, when $f\left(x\right)=x^3-6x^2+11x-6$ is divided by $g\left(x\right)=x-1$ we get remainder 0.
Hence, x - 1 is a factor of $x^3-6x^2+11x-6.$