Question

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

Answer 1

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

Cancel to get `(x-5)/(x-2)`