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Question

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+x22x1,g(x)=x+1
(ii)p(x)=x3+3x2+3x+1,g(x)=x+2 [4 MARKS]


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Solution

Concept: 1 Mark
Application: 1.5 Marks each

(i)p(x)=2x3+x22x1,g(x)=x+1

p(1)=2(1)3+(1)22(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=10.

Therefore, by the Factor Theorem, (x+2) is not a factor of p(x).


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