## 1. Activity 9: Polynomials

### 1.1. What are the important features of a polynomial graph we typically identify?

1.1.1. How do we identify these components?

### 1.2. How do you identify key features WITHOUT using a graphing calculator?

### 1.3. What is multiplicity?

1.3.1. How does it affect a polynomial?

### 1.4. What are similarities/differences of zeros, x-intercepts, and factors?

## 2. Activity 10: Analyzing Polynomial Functions

### 2.1. What features of a polynomial function can help you sketch a graph?

### 2.2. What is the Rational Root Theorem?

2.2.1. Why/when do we use it?

2.2.2. How do we use it?

### 2.3. What is Descartes' Rule of Signs?

2.3.1. Why/when do we use it?

2.3.2. How do we use it?

## 3. Activity 11: Complex Roots and Inequalities

### 3.1. What is the Complex Conjugate Theorem?

### 3.2. What is the difference between factored and standard form?

### 3.3. How do you solve for zeros of a polynomial?

3.3.1. What are the difference between real/complex zeros?

3.3.2. When/why is the Rational Root Theorem useful in solving?

3.3.3. When/why is synthetic division useful in solving?

3.3.4. When/why is the Quadratic Formula helpful in solving?

### 3.4. What do polynomial inequalities tell us about a function?

3.4.1. What is the process to solve a polynomial inequality?

3.4.2. How do we write our answers to polynomial inequalities?

3.4.3. How does the initial problem set-up affect how we solve/answer a polynomial inequality (being less than versus less than or equal to)?