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

Aug 27, 2016

We have to factorise to get $\frac{x - 5}{x - 2}$

#### 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
$\frac{\left(x - 2\right) \left({x}^{2} - 25\right)}{\left(x - 2\right) \left({x}^{2} + 3 x - 10\right)}$=

$\frac{\left(x - 2\right) \left(x - 5\right) \left(x + 5\right)}{\left(x - 2\right) \left(x + 5\right) \left(x - 2\right)}$

Cancel to get $\frac{x - 5}{x - 2}$