Given:
f(x)=x3−6x2+11x−6 and g(x)=x−1
g(x)=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(x)=x3−6x2+11x−6 is divided by g(x)=x−1 we get remainder 0.
Hence, x - 1 is a factor of x3−6x2+11x−6.