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

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

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

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

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

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

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

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

There's no second degree term of the y.

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.

We have one second degree term over right there.

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

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.

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

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.

And to some degree that second explosion tends to back that up.

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

The second is giving extra money to people who get their master's degree.

So, in general, you've already learned how to factor a second degree equation.

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

Rotation degree

One Degree

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.

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.

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?

Degree of fuzzyness

to do my financial degree and my second year of university I couldn't find any job on campus.

I have this polynomial in the denominator here.

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

line to the data, we might decide that it's better to fit a quadratic function or a second order polynomial to this data.

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.

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 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.

On the bottom right, you see a robot performing a 360 degree flip in less than half a second.

I studied architecture, then did a second degree in architecture, and then actually quickly realized that it wasn't architecture.

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

Select the rotation degree.

90 degree rotation speed

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

And the reason is, what we've done is, we've fit this extra the parameter d, that is this degree of polynomial, and we'll fit that parameter d using the test set.

So a binomial is just a polynomial with two terms.