This right here is a second degree polynomial.

If you take a second degree polynomial, take its derivatives and add and subtract, you should hopefully get another second degree polynomial.

And so I'm assuming this is a second degree polynomial.

And I end up with a three term, second degree polynomial.

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

You can do this really for any degree polynomial dividing into any other degree polynomial.

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

So for example, that polynomial right there is a third degree polynomial.

Why is that a third degree polynomial?

The first terminology is the degree of the polynomial.

So let me write a fifth degree polynomial here.

So, once again, this is a fifth degree polynomial.

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

So that's where we get it's a third degree polynomial.

So this tells us this is a fifth degree polynomial.

So we end up with this nice little fifth degree polynomial.

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

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

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

This is the standard form of the polynomial where you have it in descending order of degree.

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.

In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial.

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

And this is the second degree term.

like any polynomial.

And at least, in my mind, the reason why I care about the degree of a polynomial is because when the numbers get

There's no second degree term of the y.

It's the coefficient on the second degree term.

We've simplified this polynomial.

We've simplified this polynomial.

For example, over the integers modulo , the derivative of the polynomial is the polynomial .

For example, formula_1 is a homogeneous polynomial of degree 5, in two variables the sum of the exponents in each term is always 5.

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.

Our coeffient on the second degree term here is one.

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Here, you're going to have your constants' place, your first degree place, your second degree place, your third degree place, if there is one.

The term polynomial is more general.

And then one last part to dissect the polynomial properly is to understand the coefficients of a polynomial.

Our coeffient, Our coeffient on the second degree term is one

And to some degree, your second answer would be more correct.

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.

This is the polynomial function below it.

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.

It's given by this polynomial expression right here.

So to find the opposite of this polynomial,