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The problem asks to find a degree 5 polynomial \( f(x) \) with the given zeros: \( 0, 2, 4, -1, 7 \), and to leave the answer in factored form.

When you know the zeros of a polynomial, the corresponding factors are of the form \( (x - \text{zero}) \). So, for each zero given:

- \( 0 \) corresponds to \( x \),
- \( 2 \) corresponds to \( (x - 2) \),
- \( 4 \) corresponds to \( (x - 4) \),
- \( -1 \) corresponds to \( (x + 1) \),
- \( 7 \) corresponds to \( (x - 7) \).

Thus, the polynomial in factored form is:

\[
f(x) = x(x - 2)(x - 4)(x + 1)(x - 7)
\]

Let me know if you'd like further details or have questions!

Here are 5 related questions you might find useful:
1. How can you expand this polynomial into standard form?
2. What is the degree of the polynomial and why?
3. How does the multiplicity of zeros affect the shape of the polynomial's graph?
4. What happens if one of the zeros is repeated (i.e., has a multiplicity greater than 1)?
5. How can you find the y-intercept of this polynomial?

**Tip:** The y-intercept of a polynomial is always the constant term when the polynomial is in standard form.

Find a polynomial f(x) of degree 5 that has the following zeros: 0, 2, 4, -1, 7. Leave your answer in factored form.

Learn how to find the polynomial f(x) of degree 5 with the given zeros 0, 2, 4, -1, and 7 in its factored form. This problem covers key concepts in algebra, including polynomial factoring and the fundamental theorem of algebra. Suitable for students in Grades 9-12.

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