Question

If p(x)=x^4+x^3+x^2-5x+1 and s(x)=x+1,find the remainder when p(x) is divided by s(x)

Answer 1

We need to apply remainder theorem.
p(x)=x^4+x^3+x^2-5x+1
s(x)=x+1
So as the remainder theorem says
the remainder is p(-1)
p(-1)= (-1)^4+(-1)^3+(-1)^2-5(-1)+1
p(-1)=1-1+1+5+1=7
Therefore, the remainder is 7