Question

Let p(x) = 2x − x3 and q(x) = x4 − 2x2 + 2x. Find a polynomial f(x) ∈ Q[x] such that it leaves remainder x2 +x when divided by p(x) and it leaves remainder x when divided by q(x).

Answer 1

Answer:

2x-3x=x4-2x2+2x

x=8x

x*x=8