How to divide certain polynomials? Can somebody help me with this question?
$$\frac{15p^3+16p^2+46}{3p+5}$$
For some reason I can't wrap my head around the process used to divide polynomials, I can do long division but every time somebody explains the long division of polynomials to me I can't understand it whatsoever.

$\color{red}{\rm Reds}$ are the terms we want to kill, $\color{blue}{\rm blues}$ are pieces of our answer.
Consider $\color{red}{15p^3}+16p^2 + 46$. If I multiply $3p+5$ by $\color{blue}{5p^2}$, we get $\color{red}{15p^3}+25p^2$.
Subtracting it, we're left with $\color{red}{-9p^2}+46$. If I multiply $3p+5$ by $\color{blue}{-3p}$, we get $\color{red}{-9p^2}-15p$.
Subtracting it, we're left with $\color{red}{15p}+46$. If I multiply $3p+5$ by $\color{blue}{5}$, we get $\color{red}{15p}+25$.
Subtracting it, we're left with $\color{green}{24}$. Since the degree of $24$ is less than the degree of $3p+5$, the process ends.
$$15p^3+16p^2 + 46 = (\color{blue}{5p^2-3p+5})(3p+5)+\color{green}{24}.$$
How we find our $\color{blue}{\rm blue}$ terms? Look at the leading terms. In each step: $$\frac{\color{red}{15p^3}}{3p} = \color{blue}{5p^2}, \quad \frac{\color{red}{-9p^2}}{3p} = \color{blue}{-3p}, \quad \frac{\color{red}{15p}}{3p} = \color{blue}{5}.$$
