Question

The remainder when polynomial P(x) of degree 5 is divided by x+1 and x-1 is 1 and 2 respectively. What is the remainder when the same polynomial is divided by x^2-1.

Answer 1

Let the remainder when p(x) is divided by x^2-1 be r(x), then;

r(x) = p(x^2) = p(1)

or, p(x) = p(root 1) = p(1)

Hence, the remainder would be p(1) and we are provided with the information that p(1) = 2.

HOPE THIS COULD HELP!!!