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Question

Use the Factor Theorem to determine whether g(x) is factor of f(x):
f(x)=x3+3x2+3x+1,g(x)=x+1

Solution
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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+33+1
or,f(1)=0
So g(x)=x+1 is factor of f(x)=x3+3x2+3x+1

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