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So here are the topics that I'm 
going to talk about this week.

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Again each one roughly covers 
2 minutes, so if you want to

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skip forward to that part in the talk, you can.

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We're going to start with a 
couple of polynomial statements

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that I'm not going to prove 
but that are pretty important,

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and then as you can see here, we 
have - what is this, 6 named theorems.

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So Remainder Theorem, Factor Theorem,

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Roots Over a Field which arguably is

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just as important as some 
of these other theorems

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but doesn't have a name, 
Fundamental Theorem of Algebra,

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Complex Polynomials of 
Degree n Have n Roots,

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then the proof of that, the Rational Roots 
Theorem, and the Conjugate Roots Theorem.

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So notice in the middle here, 
I've kind of glossed over this 

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but Fundamental Theorem of Algebra is 
one of the more important statements

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in mathematics. Fundamental - 
anything Fundamental Theorem of

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blah, that's probably a pretty important 
theorem and you should know it.

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That's all I really have to say. Here 
we'll talk a little bit more about the

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Fundamental Theorem
of Algebra in a minute.

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We won't talk about the proof. The 
proof is just a little bit beyond what

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we want to do in this course.