How do you simplify #(x^3-2x^2-25x+50)/(x^3+5x^2-4x-20)#?
We have to factorise to get
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
Cancel to get