Learning Objectives:

__Math Tutoring on Finding the Zeros of Polynomial Functions__

Let us find the connections among the real rational **zeros**, the factors and the graphs of **polynomial functions.**

To begin, let us assume we have a **polynomial function** of degree **n, **

and **c** is a real number such that **f(c) = 0.** So if we substitute the value of **c **into the **function,** the **function **value is **zero**. So we say,

**1.** The real number **c** is a **zero** or root of the **polynomial function f(x).**

**2. x = c** is a solution to the equation **f(x) = 0. **

**3.** The quantity **(x – c)** is a factor of the **polynomial function f(x). **

**4.** The point **(c, 0)** is an **x** intercept of the graph of the **polynomial function f(x). **

Also a **polynomial function** of degree **n **with complex coefficients in the form

has exactly **n** complex **zeros**, counting multiplicity. This is the **Complex Factorization Theorem. **

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**Hook Questions**:

*1. **What are the zeros of a polynomial function?*

*2. **`What are the zeros of a polynomial?*

*3. ** What is a simple zero?*

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