exam Maths Puzzle Numerical Ability

Perform the indicated divisions.
8x^3 -6x^2 + 2x / 4x +1
This is what I got is it right?
2x^2 - 2x + 1

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exam Other Question

Hi! This is the question:
Is U= The set of all polynomials in P3 with constant term 0, a subspace of P3?

I said yes because 0 lies in U, the addition of any 2 polynomials from since i didnt understand the multiplying part, i didnt really understand the division part either, would be cool if someone could also explain this problem to me; x^2+5x+4/(x+3)^2 divided by x+1/x^2-9.