Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i)p(x)=2x3+x2−2x−1,g(x)=x+1
(ii)p(x)=x3+3x2+3x+1,g(x)=x+2 [4 MARKS]
Concept: 1 Mark
Application: 1.5 Marks each
(i)p(x)=2x3+x2−2x−1,g(x)=x+1
p(−1)=2(−1)3+(−1)2−2(−1)−1=0
Therefore, by the Factor Theorem, (x+1) is a factor of p(x).
(ii)p(x)=x3+3x2+3x+1,g(x)=x+2
p(−2)=(−2)3+3(−2)2+3(−2)+1=−1≠0.
Therefore, by the Factor Theorem, (x+2) is not a factor of p(x).