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Question

Find the remainder when x3+3x2+3x+1 is divided by:
(i)x+1
(ii)5+2x [4 MARKS]


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Solution

Concept: 1 Mark
Application: 3 Marks

(i) Let p(x)=x3+3x2+3x+1 and q(x)=x+1

According to Remainder Theorem, remainder is equal to p(a) when p(x) is divided by (xa).

p(1)=(1)3+3(1)2+3(1)+1=1+33+1=0

Therefore, remainder is 0 when p(x)=x3+3x2+3x+1 is divided by x+1


(ii)Let p(x)=x3+3x2+3x+1 and q(x)=5+2x

p(52)=(52)3+3(52)2+3(52)+1

=(1258)+(754)+(152)+1

=(125+15060+88)=(278)

Therefore, remainder is equal to (278) when p(x)=x3+3x2+3x+1 is divided by 5+2x (Using Remainder Theorem)


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