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To solve for the zeros of the polynomial function \( h(x) = 5x^3 + x^2 - 20x - 4 \), we can apply the **Rational Root Theorem** and then use synthetic division to find all zeros.

### Steps:

1. **Rational Root Theorem**: According to this theorem, any rational root, in the form \( \frac{p}{q} \), is a factor of the constant term (-4) divided by a factor of the leading coefficient (5).

   - **Factors of -4**: \( \pm 1, \pm 2, \pm 4 \)
   - **Factors of 5**: \( \pm 1, \pm 5 \)

   Possible rational roots are: \( \pm 1, \pm 2, \pm 4, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5} \).

2. **Testing Possible Rational Roots**: Let's start by testing these values in \( h(x) \) until we find a root.

   After testing, we find that \( x = 1 \) is a root, since:
   \[
   h(1) = 5(1)^3 + (1)^2 - 20(1) - 4 = 5 + 1 - 20 - 4 = -18 \neq 0
   \]

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The function below has at least one rational zero. Use this fact to find all zeros of the function. h(x) = 5x^3 + x^2 - 20x - 4. If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

Learn how to find all zeros of the polynomial function h(x) = 5x^3 + x^2 - 20x - 4 using the Rational Root Theorem. This problem provides a step-by-step solution to identify rational roots, suitable for students in Grades 10-12.

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