Alternating polynomial

An alternating polynomial is like a math problem where you add and subtract things that look like x to the power of a number.

Let's start with regular x and a number like 2. This means you have x squared, which is like saying you have two x's that you multiply by each other. So, the first term in our alternating polynomial would be x squared.

Now, let's add another term but instead of just x squared, it's negative x to the power of 3. This means you have three x's that you multiply by each other, but one of them is negative. So, the second term in our alternating polynomial would be negative x cubed.

Next, we add another term but we go back to x squared, like before. And we keep doing this, alternating between x squared and negative x cubed, again and again.

So, an alternating polynomial is just a bunch of terms where you have some positive power of x and then the next term has the same thing but with a negative sign in front of it. You keep going back and forth like this until you run out of terms.

And that's all there is to it!