How do you use synthetic division to divide `(14x^2 - 34) / (x + 4)`?

The premise

given factor `(x-a)` to `f(x)=Bx^2+Cx+D`,

The pink arrow means multiply `a` by whatever the difference of the previous column's value was (it's subtraction).
You start out with taking `B` and putting it in the difference row, so the next column will be `C-aB`. The next column should be `D-a(C-aB)`, and so on. This applies to all polynomial equations.

Also, you CANNOT miss a term, so if you have something like `3x^5+8x^3-2x^2` you would have to write in 0s for the missing terms...
like this `\rightarrow3x^5+0x^4+8x^3-2x^2+0x-0`

Your result should have all the powers of `x` shifted down one degree, so a polynomial beginning with `x^5` would have a quotient beginning with `x^4`.

If the last column does not get you a `0` as the result, then it will be the remainder, which you put over the factor you divided by, `\frac(\text(remainder))(x-a)`

Actual calculation

`14x^2-34\leftrightarrow14x^2+0x-34`
dividing by `(x+4)`; from `(x-a)` form that means `a=-4`

So we have the synthetic division set up:
-4 | 14 0 -34

----.--------.------.
`\color{white}{abc}`14

-4 | 14 `\color{white}{a}` 0 `\color{white}{abc}`-34
`-``\color{white}{abc}`(-56) `\color{white}{a}`224
---.----------.----------.
`\color{white}{abc}`14`\color{white}{ab}`56`\color{white}{abc}`258

We get `14x-56+\frac{258}{x-4}`