Find the remainder when x3+3x2+3x+1 is divided by:
(i)x+1
(ii)5+2x [4 MARKS]
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 (x−a).
p(−1)=(−1)3+3(−1)2+3(−1)+1=−1+3−3+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+150−60+88)=(−278)
Therefore, remainder is equal to (−278) when p(x)=x3+3x2+3x+1 is divided by 5+2x (Using Remainder Theorem)