How do you simplify (x^3-2x^2-25x+50)/(x^3+5x^2-4x-20)x3−2x2−25x+50x3+5x2−4x−20?

1 Answer
Annie
Aug 27, 2016

We have to factorise to get (x-5)/(x-2)x−5x−2

Explanation:

Using the factor theorem:
Try x =1: the numerator is 1-2-25+50 this is not zero so X-1 is not a factor
Try x =2: the numerator: 8-8-50+50=0 thus X-2 is a factor
Is X-2 factor of the denominator? Try X=2 :8+20-8-20=0

Use division or synthetic division to arrive at
((x-2)(x ^2-25))/((x-2)(x ^2+3x-10))(x−2)(x2−25)(x−2)(x2+3x−10)=

((x-2)(x-5)(x +5))/((x-2)(x+5)(x-2))(x−2)(x−5)(x+5)(x−2)(x+5)(x−2)

Cancel to get (x-5)/(x-2)x−5x−2

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