How do you factor $r^3-5r^2-100r+500$ ?

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Answer 1 · 2017-02-09T09:16:29

The answer is $=(r-10)(r-5)(r+10)$

Let $f(r)=r^3-5r^2-100r+500$

$f(10)=100-500-100+500=0$

So, $(x-10)$ is a factor of $f(r)$

To find the other factors, we do a long division

$color(white)(aaaa)$ $r^3-5r^2-100r+500$ $color(white)(aaaa)$ $|$ $r-10$

$color(white)(aaaa)$ $r^3-10r^2$ $color(white)(aaaaaaaaaaaaaaa)$ $|$ $r^2+5r-50$

$color(white)(aaaaa)$ $0+5r^2-100r$

$color(white)(aaaaaaa)$ $+5r^2-50r$

$color(white)(aaaaaaaaa)$ $+0-50r+500$

$color(white)(aaaaaaaaaaaaa)$ $-50r+500$

$color(white)(aaaaaaaaaaaaaaa)$ $-0+0$

Therefore,

$f(r)=(r-10)(r^2+5r-50)$

$=(r-10)(r-5)(r+10)$

How do you factor r^3-5r^2-100r+500r^3-5r^2-100r+500?