How do you divide a polynomial by a binomial of the form $ax^2+b$, where $a$ and $b$ are greater than one? I came across a question that asked me to divide $-2x^3+4x^2-3x+5$ by $4x^2+5$. Can anyone help me?

You can do long division with polynomials almost the same way you would for integers. For example, $4x^2+5$ can be multiplied by $-\frac{1}{2}x$ to get a leading term of $-2x^3$, so we might say that $4x^2+5$ goes into $-2x^3 + 4x^2 - 3x + 5$ about $-\frac{1}{2}x$ times. As with long division, we then multiply $4x^2+5$ by $-\frac{1}{2}x$ and subtract the result from $-2x^3 + 4x^2 - 3x + 5$; then repeat the process until we can't anymore. If there's a remainder at the end, we divide it by the divisor and add that to the end of the result (again, similar to long division).
In this case you should verify that the result is $-\frac{1}{2}x + 1 + \frac{-x}{8x^2+10}$.
