If F is algebraically closed, show Alg ext is closed too

[Mr Davis 97]

Homework Statement

Let E be an algebraic extension of F in which every polynomial in F[x]
can be factored into linear polynomials. Then E is algebraically closed.

Homework Equations

The Attempt at a Solution

This seems like a very easy problem, but I'm not sure how to write things down formally.

 

[fresh_42]

Homework Statement

Let E be an algebraic extension of F in which every polynomial in F[x]
can be factored into linear polynomials. Then E is algebraically closed.

Homework Equations

The Attempt at a Solution

This seems like a very easy problem, but I'm not sure how to write things down formally.

Start with the definition that you use: What is an algebraic closed field? What is an algebraic extension? How do they relate to F?

That's why we have "

Homework Equations

" above. It's meant to tell us which definitions and notations you are used to. "This seems like a very easy problem" because it could well be the definition. Thus the question about your definition is the crucial part.