And I don't know exactly what this third degree polynomial

Now a third degree polynomial can have as many as three 0's.

They say it's a third degree polynomial of the form ax to the third plus bx squared plus cx plus d.

I've chosen the degree d of polynomial using the test set.

So this one must have a third real 0, because if the third one was complex, you'd need another complex 0, and you can't have four 0's for a third degree polynomial.

And that's what's actually called a quadratic equation, or this second degree polynomial.

Let's say you try to choose what degree polynomial to fit to data.

Sometimes a quadratic polynomial, or just a quadratic itself, or quadratic expression, but all it means is a second degree polynomial.

After every step we're canceling out the largest degree of the polynomial we're dividing into.

For example, if you use polynomials this might be a high degree polynomial over here and maybe a linear function over here which is a low degree polynomial your training data error tends to go like this.

So the first thing is to think about, is what would a third degree polynomial look like and what are we even talking about when we say 0's.

And so this degree of polynomial, so the parameter is no longer fit to the test set.

The suspect was given the third degree until he confessed his crime.

I was in the third year of my seven year undergraduate degree.

like the degree polynomial to use with the learning algorithm or choose the regularization parameter for learning algorithm.

If we have a very high degree of polynomial, our training error is going to be really low.

That is, if d the degree of polynomial was too large for the data set that we have.

But here, you can do from UNlNTELLlGIBLE the highest degree term here is a second degree term, here it's a third degree term, so we're cool.

The next thing to do, if we're going to decompose this into its components, we have to figure out the factors of the denominator right here, so that we can use those factors as the denominators in each of the components, and a third degree polynomial is much, much, much harder to factor than a second degree polynomial, normally.

On the horizontal axis I am going to plot the degree of polynomial, so as I go the right

Now, if we have a third degree polynomial where these three x values make it 0, we can rewrite this third degree polynomial as we can rewrite it as I'll do it in a slightly different color f of x is equal to x plus 1 you'll see why I'm doing x plus 1 instead of x minus 1 in a second x plus 1 times x minus 2 times x minus r3.

Let's say this is my polynomial, let me call my polynomial p of x.

In this video I want to do a bunch of examples of factoring a second degree polynomial, which is often called a quadratic.

Rotation degree

One Degree

1.2 degree.

Degree of fuzzyness

By what degree?

I have this polynomial in the denominator here.

So in that case, I'm going to pick this fourth order polynomial model and finally what this means is that that parameter d, remember d was the degree of polynomial, right d equals 2, d equals 3, up to d equals 10.

Suppose you like to decide what degree of polynomial to fit to a data set, sort of what features to include to give you a learning algorithm.

A has a degree of 3, B has a degree of 2, D has a degree of 3, and C has a degree of 2.

low order polynomial such as a plus one, when we really needed a higher order polynomial to fit the data.

Third!

Select the rotation degree.

90 degree rotation speed

Really, 180 degree change

So it's as if there's one extra parameter in this algorithm, which I'm going to denote d, which is what degree of polynomial do you want to pick?

Let's say I'm defining, so this is a polynomial.

So that is a 90 degree angle, a 90 degree angle and that is a 90 degree angle over there

It's easy to get a 90 degree angle a tron, and if I take a third of a third of that, that's a ninth of 90 which is another 10 degrees.

And so as we increase of the greater polynomial we find typically that the training error decreases, so I'm going to write j subscript train of theta there, because our training error tends to decrease with the degree of the polynomial that we fit to the data.

third...third prize,middle school spelling bee.

So this first degree so this is going to be a 0 degree or a constant term Here the degree is 2.

This isn't too hard we just make a note that degree centrality just means that degree which node has the highest degree.