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.

There are two ways to approach this.
The "long" way is to do polynomial long division. It's not that difficult if you just consider the lead coefficients when you're deciding the "how much into" part, but take the whole expression into account when subtracting. Rather than trying (and very likely failing) to typeset the whole thing in my rudimentary Latex, I'll just link you to this: http://www.purplemath.com/modules/polydiv2.htm
The "short" way, which is what I'll highlight here, is something called synthetic division, which works only when you have linear (degree one) factors in the divisor. In this case, this works fine, but you have to ensure the lead coefficient of the divisor is reduced to one by dividing throughout by $3$. Here's the link for synthetic division: http://www.purplemath.com/modules/synthdiv.htm
You might find synthetic division much easier because you're dealing only in numbers (the coefficients) and adding rather than subtracting. Keep in mind that if you divided both numerator and denominator by a constant to get a monic linear factor in the divisor (for synthetic division), your quotient will not be affected but your remainder will. So you must multiply by that constant to get the remainder for the original division problem.
