Question

How do you long divide `(x^2-18x+80)` by `x-10`?

Answer 1

There is more than one way. One that I am used to do is factoring. We factor the numerator (your quadratic) and proceed as follows.

In order to factor, we must find the roots:

`(18+-sqrt(18^2-4(1)(80)))/2`
`(18+-2)/2`
`x_1=10`, which is the same as the factor `x-10=0`
`x_1=8`, which is the same as the factor `x-8=0`

Then, your division gets way simpler:

`((x-8)cancel(x-10))/cancel(x-10)=color(green)(x-8)`