Question

how to show that a polynomial does not have any rational zeros

Answer 1

That really depends. What is the degree of the polynomial?

Answer 2

Is it a quadratic (degree 2)? Is it cubic (degree 3)? OMG quartic (degree 4)!?

Answer 3

Are you ignoring me because you are waiting for someone to give the answer or because you don't understand what I'm asking you?

Answer 4

Im busy doing homework and check back every so often, RUDE. I actually do my homework.

Answer 5

Haha well, good =) I apologize. What degree polynomial are you working with?

Answer 6

That is degree 3 because the highest exponent is 3.

Answer 7

p(x) = x^3 -x -2

Answer 8

Also cubic.

Answer 9

Okay, Lanik. So, there's this cool way that we can list all of the POSSIBLE rational zeroes of a polynomial. Are you aware of it?

Answer 10

Yes. Can we get to the point ( not trying to be rude)

Answer 11

The process is simply:
List all possible rational zeroes.
Check each one.

Answer 12

Can I see your attempt at listing the possible rational zeroes?

Answer 13

I JUST NEED TO KNOW HOW TO DO THE PROBLEM, you don't even have to do it for me.

Answer 14

...I'm explaining how.

Answer 15

continue.

Answer 16

If you don't know how to list the possible rational zeroes, then I will explain, but you DID say that you know how already.

Answer 17

yes..

Answer 18

I'll remind you. Look at the last term, which in this case is 2. Look at the first coefficient, which in this case is 1.
Possible rational roots MUST be something like:
\[\frac{\text{factor of the last term}}{\text{factor of the first coefficient}}\]

Answer 19

Quick example:
For the polynomial
x^3 + 4x^2 -16x + 8
what are the possible rational zeroes?
The last term is 8. The first coefficient is 1. Well, I look at the factors of 8, and divide by the factors of 1.
Factors of 8: 1,2,4,8 (positive or negative)
Factors of 1: 1 (positive or negative)

So the possible zeroes are 1,-1,2,-2,4,-4,8,-8