Q&A for How to Divide Polynomials

You can always add + 0 to the polynomial if you find having that placeholder helpful. Otherwise, the same steps all work, just remember 0 times anything is 0.

Use the Remainder Theorem to turn this into an easier problem: Call that polynomial f(x), then the Remainder Theorem implies f(2) = 20. f(2) = 2*(8) + 4 - 3*(2) + p = 14 + p. If 14 + p = 20, then p = 6 and you don't actually have to work through an ugly polynomial division.

Factor Q using the difference of cubes factorization trick. But isn't Q is a sum of cubes, not a difference so the trick doesn't apply here? No problem, because we can consider -y instead of +y and then it is the difference of cubes! Q(x) = x^3 + y^3 = x^3 - (-y)^3 = [x-(-y)]*[x^2 + x(-y) + (-y)^2] = (x+y)(x^2 - xy + y^2).

(x³ + x² + 10x - 8) / (x + 4) = x² - 3x + 22 - [96 / (x + 4)].