P(x) = x^4 + (2-a)x^3 + (3-2a)x^2 - 2x + a

Divide the polynomial by x^2 + 2x + 2, and find the remainder

Hence, deduce that x^4 - 2x^2 + 2 is divisible by x^2 + 2x + 2 and factorise P(x) completely into real factors.

Thanks for any help. I started to use synthetic and algorithm division, but it just turned into a mess