# How do you use synthetic division to divide x^4 – 8x^3 + 16x^2 – 19 by x-5?

May 28, 2015

Synthetic Division is preformed in much the same manner as long division.
Note, however, the need to include all powers of $x$ even when their coefficient is $0$.

Hopefully the following image will demonstrate the process (because generating the series of step-by-step images is a lot of work)

So $\left({x}^{4} - 8 {x}^{3} + 16 {x}^{2} - 19\right) \div \left(x - 5\right)$

$= \left({x}^{3} - 3 {x}^{2} + x + 5\right)$ with a Remainder of $6$

or
$= \left({x}^{3} - 3 {x}^{2} + x + 5\right) + \frac{6}{x - 5}$