C3 Algebra Division question

I'm trying to solve this:

$\frac{8x^3+2x^2+5}{2x^2+2}$

But the divisor is awkward and I'm stuck. Please could you show me how to do it using long division?

(I started by dividing 8x^3 by 2x^2 to get the first term of the answer, 4x, then I multiplied this by 2x^2+2 to get the part which you have to takeaway, which is 8x^3+8x. So the 2x^2 in the original equation got skipped out and then I just carried on but I got a negative power so it's all gone a bit bad)

I'm trying to solve this:

$\frac{8x^3+2x^2+5}{2x^2+2}$

But the divisor is awkward and I'm stuck. Please could you show me how to do it using long division?

(I started by dividing 8x^3 by 2x^2 to get the first term of the answer, 4x, then I multiplied this by 2x^2+2 to get the part which you have to takeaway, which is 8x^3+8x. So the 2x^2 in the original equation got skipped out and then I just carried on but I got a negative power so it's all gone a bit bad)

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Thanks both of you - I was only using 0 coefficients for the numerator, and using them for the denominator worked So the remainder is -8x+3[\tex]?

Also one more thing - I tried using the remainder theorem to find the remainder but when I set the divisor equal to 0, I got sqrt -1. Did I do this right? (is it not possible to use the remainder theorem in this case?)