Rational root theorem

Question

Using the Rational Root Theorem, list all the possible rational roots of the polynomial.

m(x)=6x^3+x^2-x+2

Answer 1

The Rational Root Theorem statates that every rational root must be of the form

p/q, where

p must divide the constant term 2, and

q must divide the high order term 6.

So all the possible candidates for p are 2, 1, -1, -2, and

all the possible candidates for q are 6, 3, 2, 1, -1, -2, -3, -6.

Those would allow for 32 possible roots, but many combinations are equivalent.

We can ignore all the negative divisors and then add the opposite to each positive candidate for a root.

There are 6 positive candidates for a rational root.

2/6 = 1/3

1/6

2/3

2/2 = 1/1

1/2

2/1