 So our division statement is our big polynomial, our p of x, what we're calling p of x in a division statement, is equal to the quotient times the divisor plus the remainder, p of x is equal to q of x times d of x plus r of x. Now what does this mean? It means this polynomial is equal to this polynomial times this polynomial plus 420. This function is equal to this function times this function plus this function. Graphically, this is what it would look like. One thing to keep in mind with these graphs is they're not to scale. So this guy's actually going up all the way to 420. That one's actually 420, a line, horizontal line at y is equal to 420, and these guys are smaller scales. So the scales of the Cartesian coordinate systems on all these is not the same. It's just sort of a presentation of what it looks like. So the division statement up here, what it's saying graphically is this function is made up of is equal to this function times this function plus this function. So if you multiply this graph with this graph and moved everything 420 up, 420 higher, you would get this function. And that's what the division statement is saying here, but we're saying it with terms, with letters, with numbers instead of visually as graphically. I hope this makes sense because this is really what we're getting at because polynomials and non-polynomials, basically functions in general, what we're doing is learning the different techniques to break things down and look at their core elements and mess around with functions. Take a little function from here, take another function from here, combine them and see what happens. Take one function and take another function that we may like, we may want to, you know, that we've used somewhere, right, and you know, it may represent something that we have, right? So taking one function and dividing into another function just to see what the end result is. Is the end result what we want? Is the remainder what we want, right? And keep in mind this guy here is your Y coordinate when your X's are these guys, okay? So you can break these down even further, right? You can factor these down even further, get your X values, and if those X values you plug in to original function, this is what you get out, you get 420 out, right? So there's a lot here and it's, you know, it's just a graphical way of looking at it and you know, trying to, everything that you're doing when you're doing the long division, when you're doing synthetic division, when you're doing factoring, when you're looking functions, when you're looking polynomials, what you should be doing is thinking about this in a graphical form, right? Everything that you're touching, everything that you're working with in general is going to be a function, right? As long as we're dealing with polynomials and functions, right? Numbers, no, numbers are just numbers, basic operations are just basic operations. But those are our building blocks, right? The real number set, our building blocks, variables are building blocks for us to be able to model things in real life and see how things work out. What happens when we combine functions together? What happens when we multiply functions together? What happens when we multiply functions together and translate them over, right? Moving around the Cartesian coordinate system. Do they give us what we want?