Long division of $\frac{3x^3-x^2-13x-13}{x^2-x-6}$ I'm self-studying from Stroud & Booth's amazing textbook "Engineering Mathematics", and am on the "Partial Fractions" chapter. As part of an exercise I need to do long division of two polynomial equations.
The problem is, long division of polynomials was never explained in the textbook. The long division I need to do is this one:
$$\frac{3x^3-x^2-13x-13}{x^2-x-6}$$
The book states that the result is:
$$3x+2+\frac{7x-1}{x^2-x-6}$$
But the mechanics of the long division are never explained. Can I please get some help with this one?

Polynomial long division is exactly same as long division of decimals.
With respect to your posed problem here are steps.
Step1: We have to divide $3x^3-x^2-\dots$ with $x^2$, so we first multiply the divisor $(x^2-x-6)$ by $3x$ to give $3x^3$. THen we subtract and copy the remaining terms.
Step2: Again now we have $2x^2+5x-13$ and we have to divide by $x^2-x-6$. So we multiply our divisor by $2$.
Finally, we get $3x+2$ as dividend and $7x-1$ as remainder. Now recall if we had  $\frac{17}{3}$ we would write it as $5+\frac{2}{3}$. Here $\bf{2}$ is remainder.
Similarly we write our result of long division as $$3x+2+\frac{7x-1}{x^2-x-6}$$

