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Let's address the questions based on the given information:

If \( c \) is a zero of the polynomial \( P \), here's how we can complete the statements:

(a) \( P(c) = ? \)  
Since \( c \) is a zero of the polynomial \( P \), it means \( P(c) = 0 \).

(b) \( x - c \) is a ___ of \( P(x) \).  
If \( c \) is a zero, then \( x - c \) is a **factor** of \( P(x) \).

(c) \( c \) is a(n) ___-intercept of the graph of \( P \).  
Since \( c \) is a zero of \( P \), it represents the \( x \)-intercept of the graph of \( P \).

So the completed answers are:

(a) \( P(c) = 0 \)  
(b) \( x - c \) is a **factor** of \( P(x) \).  
(c) \( c \) is an \( x \)-intercept of the graph of \( P \).

Would you like more details or have any questions about this?

Here are some related questions that might interest you:

1. How do you find the zeros of a polynomial function?
2. What is the relationship between the factors and zeros of a polynomial?
3. How do you determine the multiplicity of a zero?
4. What is the significance of the x-intercept in the graph of a function?
5. How can you use synthetic division to verify a zero of a polynomial?

**Tip:** Remember, zeros of a polynomial function correspond to the points where the graph intersects the x-axis, which are also the roots or solutions of the polynomial equation \( P(x) = 0 \).

If c is a zero of the polynomial P, then consider the following: (a) P(c) = ?, (b) x - c is a ___ of P(x), (c) c is a(n) ___-intercept of the graph of P.

Explore how to determine the zeros of a polynomial function and their role as factors and x-intercepts. Learn the connection between the factor theorem and graphing polynomials. Suitable for high school algebra students.

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