How do I continue solving this polynomial division? I had this equation as a bonus question on a quiz today. I got to a certain extend and was completely unsure how to continue.


*$$(10x^4-18x^3-94x^2-8x+2) \div (10x+2)$$


I figured the easiest first step would be to divide. (Actually, I assumed it was factorable, but I have no idea how to go about that)
$$\frac{(10x^4-18x^3-94x^2-8x+2)} {(10x+2)}$$
$$\frac{10x^4}{10x+2} + \frac{-18x^3}{10x+2} + \frac{-94x^2}{10x+2} + \frac{-8x}{10x+2} + \frac{2}{10x+2}$$
Simplifying some more (multiplying by $10x+2$)
$$10x^4-18x^3-94x^2-8x-2 = 0$$
But what do I do from here? Do I factor? Do do something else?
If I do factor How do I go about that? If not, what do I do instead?

multiples of $10 x + 2$
$$
\begin{array}{rrrrrr}
x^3 \mapsto & 10 x^4 & + 2 x^3 &&& \\
-2x^2 \mapsto & & -20 x^3 & -4 x^2 && \\
-9x \mapsto & & & -90 x^2 & -18 x & \\
+1 \mapsto & & & & 10 x & + 2 & \\
&&&&& \\
  & 10x^4 & - 18 x^3 & -94 x^2 & -8 x & + 2 & \\
\end{array}
$$
