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# What are the possible rational zeros of f(x) = 3x^{4} + x^{3} - 13x^{2} - 2x + 9?

**Solution:**

It is given that

f(x) = 3x^{4} + x^{3} - 13x^{2} - 2x + 9

The rational roots theorem states that any rational root will be a factor of the constant over a factor of the leading coefficient.

In the given equation, it is a factor of 9 over a factor of 3.

Here the factors of 9 are ±1, ±3, ±9

Factors of 3 are ±1, ±3

Therefore, the possible rational zeros are ±1, ±3, ±9, ±1/3.

## What are the possible rational zeros of f(x) = 3x^{4} + x^{3} - 13x^{2} - 2x + 9?

**Summary:**

The possible rational zeros of f(x) = 3x^{4} + x^{3} - 13x^{2} - 2x + 9 are ±1, ±3, ±9, ±1/3.

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