Question

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

Answer 1

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 `(x^4-8x^3+16x^2-19) div (x-5)`

`= (x^3-3x^2+x+5)` with a Remainder of `6`

or
`= (x^3-3x^2+x+5)+ 6/(x-5)`