If x = a is a zero of a polynomial function f, then the following statements are true.
(a) x = a is a 
---Select---
 of the polynomial equation f(x) = 0.

(b) 
---Select---
 is a factor of the polynomial f(x).

(c) The point 
---Select---
 is an x-intercept of the graph of f.

Let's fill in the blanks for each statement based on the information provided:

(a) \( x = a \) is a **solution** of the polynomial equation \( f(x) = 0 \).

(b) **\( (x - a) \)** is a factor of the polynomial \( f(x) \).

(c) The point **\( (a, 0) \)** is an x-intercept of the graph of \( f \).

Would you like more details or have any questions on these? Here are five related questions to deepen your understanding:

1. How does the Factor Theorem relate to finding factors of a polynomial?
2. Can a polynomial have more than one zero? If so, how does that affect the number of factors?
3. What happens if \( x = a \) is a repeated zero of a polynomial?
4. How do you determine if a zero is also an x-intercept on the graph of a polynomial?
5. Can a polynomial have a zero that is not an x-intercept? Why or why not?

**Tip:** Remember, if \( f(a) = 0 \), then \( x = a \) is both a solution to the equation and a factor of the polynomial.

If x = a is a zero of a polynomial function f, then the following statements are true. (a) x = a is a ---Select--- of the polynomial equation f(x) = 0. (b) ---Select--- is a factor of the polynomial f(x). (c) The point ---Select--- is an x-intercept of the graph of f.

Explore how zeros of a polynomial relate to factors and x-intercepts with step-by-step explanations. This concept uses the Factor Theorem and helps you graph polynomials. Ideal for students in Grades 9-12 learning polynomial functions.

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