Question

Divide using synthetic division, and write a summary statement in fraction form. 2x^4-x^3-15x^2+3x/x+3

Answer 1

So... first off, we sort the dividend, the numerator, in descending order... so, looking at the exponents in this one, is already sorted in descending order, from 4 down to 1, so that's done.

then the divisor, we have x+3, that means x + 3 = 0, x = -3,
so, we'll be using -3 for the synthetic division then.

$\bf \cfrac{2x^4-x^3-15x^2+3x}{x+3}\\\\ -------------------------------\\\\ \begin{array}{r|rrrrrrrrrl} -3&&2&-1&-15&3\\ &&&-6&21&-18\\ --&&-&--&--&--\\ &&2&-7&6&\boxed{-15}&\leftarrow remainder \end{array}$

and now, we'll use those coefficients, dropping the exponents of the polynomial by one, and the remainder, remains as a fraction with the divisior of x+3.

$\bf 2x^3-7x^2+6x-\frac{15}{x+3}$