Use the Factor Theorem to determine whether g(x) is factor of f(x):
f(x)=x3+3x2+3x+1,g(x)=x+1
Given polynomial f(x)=x3+3x2+3x+1 and g(x)=x+1
If x+1 is factor then f(−1)=0
Replace x in p(x) by −1 we get
f(x)=x3+3x2+3x+1
or,f(−1)=(−1)3+3(−1)2+3(−1)+1
or,f(−1)=−1+3−3+1
or,f(−1)=0
So g(x)=x+1 is factor of f(x)=x3+3x2+3x+1