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)#