Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 10x^5 + 8x^4 - 15x^3 +2x^2 - 2

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 .

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