(4x^3 + x^2 + 8x + 4) / (x^2 + 2)

The long division as follows:

4x

_______________________

(4x^3 + x^2 + 8x + 4)

4x^3 + 8x

________

??

Due to truncation of text, the (x^2 + 2) is not shown in the long division diagram.

The workings:

4x (x^2 + 2) = 4x^3 + 8x

I'm stuck with the second step. What about the ^2 exponent?

The answer key given is 4x + 1 Remainder 2

Please help. Thanks.