### 1.

What does it mean for an extension field $$E$$ of a field $$F$$ to be a simple extension of $$F\text{?}$$

### 2.

What is the definition of a minimal polynomial of an element $$\alpha\in E\text{,}$$ where $$E$$ is an extension of $$F\text{,}$$ and $$\alpha$$ is algebraic over $$F\text{?}$$

### 3.

Describe how linear algebra enters into this chapter. What critical result relies on a proof that is almost entirely linear algebra?

### 4.

What is the definition of an algebraically closed field?

### 5.

What is a splitting field of a polynomial $$p(x)\in F[x]\text{?}$$