Polynomials

You can use an online calculator for that, the solution, and the calculator can be found at:

https://www.emathhelp.net/calculators/algebra-1/polynomial-long-division-calculator/?numer=5x%5E9+-+4x%5E2+%2B2&denom=5x%2B10

Under is screengrab of the answer:

The answer to Your puzzle is thus:

\(-\frac{644x}{5} + \frac{1288}{5} - \frac{2574}{5x + 10}\)

It really is a tedious task to go through all of that.

Sorry, but you don't need to go through all that.

g(x) = (5x + 10)(q(x)) + r(x)

r(x) has to be a constant, so let's set it equal to the variable, y.

g(-2) = y = -2560 - 16 + 2 = -2574 as our remainder.