Determine all possible rational solutions of the polynomial equaiton

Question

f(x)=2x^3-5x^2+7x-5

Answer 1

all possible rational solutions are determined by using the factors of that last coefficient OVER the factors of the first coefficient. 

 

factors of last coefficient

factors of first coefficent

 

So that would be factors of 5 over factors of 2

 

factors of 5

factors of 2

 

so factors of 5...numbers that can be used for the top are 5, -5, 1 and -1

 

factors of 2...numbers that can be used for the bottom are 2, -2, 1 and -1

 

 

so then you make all possible combinations of those.

 

5/2,  5/-2,  5/1,  5/-1

 

-5/2,  -5/-2,  -5/1,  -5/-1

 

1/2,  1/-2,  1/1,  1/-1

 

-1/2,  -1/-2,  -1/1,  -1/-1

 

then you reduce all of those and only list the ones that repeat once

 

so you end up with

 

5/2,   -5/2,   5,  -5,  1/2, -1/2,  1, -1

 

Hope that helps.

 

Let me know if I need to explain any of that better

 

Kathy  :-)