Remainder and quotient of polynomial division in $\mathbb Z_7[x]$

Question

Find the quotient and remainder of:

$$ \frac {x^4 + [3]x^3 + [5]x} {x^2 + [2]} ; \mathbb Z_7[x]$$

Would the answer be the same if it wasn't in $\mathbb Z_7[x]$. Namely:
Quotient: $x^2 +[3]x - [2]$
Remainder: $[-1]x+[4], or, [6]x + [4]? $