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

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Answer 1 · 2015-05-22T22:10:20

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:

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

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