# What are the possible rational zeros of f(x) = x^{4} + 2x^{3} - 3x^{2} - 4x + 18?

**Solution:**

It is given that

f(x) = x^{4} + 2x^{3} - 3x^{2} - 4x + 18

We have to determine all the possible roots of the given function

From the rational root theorem test

We should factor the leading coefficient and constant term

In the given equation

Leading coefficient = 1

Constant term = 18

Factors of 18 (p) = 1, 2, 3, 6, 9, 18

Factor of 1 (q) = 1

Let us divide each factor of 18 by each factor of 1

The possible root is ± p/q

So the rational roots are - ±1, ±2, ±3, ±6, ±9, ±18.

Therefore, the possible rational zeros are ±1, ±2, ±3, ±6, ±9, ±18.

## What are the possible rational zeros of f(x) = x^{4} + 2x^{3} - 3x^{2} - 4x + 18?

**Summary:**

The possible rational zeros of f(x) = x^{4} + 2x^{3} - 3x^{2} - 4x + 18 are ±1, ±2, ±3, ±6, ±9, ±18.

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