Given:
The function is:

To find:
All the possible rational zeros for the given function by using the Rational Zero Theorem.
Solution:
According to the rational root theorem, all the rational roots are of the form
, where p is a factor of constant term and q is a factor of leading coefficient.
We have,

Here,
Constant term = -2
Leading coefficient = 10
Factors of -2 are ±1, ±2.
Factors of 10 are ±1, ±2, ±5, ±10.
Using the rational root theorem, all the possible rational roots are:
.
Therefore, all the possible rational roots of the given function are
.
Yes it is a rational number
Number ----- factor
1000 2
500 2
250 2
125 5
25 5
5 5
1
So the answer is 2*2*2*5*5*5 = 2^3*5^3