p(x) = x³ + 3x² + 1
g(x) = x - 2
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Given polynomial f(x)=x 3+3x 2+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)=x 3+3x 2+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)=x 3+3x 2 +3x+1
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