 We got 27 divided by 2. Now that's a straight up, you know, fraction and what we could do is try to break 27 down It's prime numbers and prime numbers, you know, it breaks down into What is a breakdown of 27 three times three times three times three gives you 27 and that doesn't reduce anymore, right? If you're doing the prime factorization, right prime trees So you could either express it like that as a number 27 divided by 2 or you could write it as a mixed number, right? there would be an integer up front and You know, if it doesn't go in completely you would have to write it as a fraction and that's what exactly what we're going to do, right? Now while we're doing this just imagine that the top 27 was actually a polynomial and the bottom was a polynomial as well We're the degree of the bottom polynomial is smaller in the degree of the top Right because that's it in that case you can actually do the division, right? So what we're gonna do is do long division for this to break this down To break it down into its mixed number, right? We actually want to find out what 27 divided by 2 is now you should know how to do this But you know in your mind right now, it's gonna be 13 and a half But we're gonna go through long division actually do it Okay, so the long division statement the way the way you express is the following So the way you write it out is to and that's your division statement. That's not a root symbol, okay? That's divided so 27 divided by 2 you read the sort of backwards 27 divided by 2 or 2 how many times does to go into? 27 now we did a video of this in the first series and it's quite simple as long division It's just takes a few steps to do so what you're gonna do is and you're gonna ask yourself Does that to go into the first number in this case? It does if it didn't you would go on to the next number and see how many times would go into the next number So how many times does to go into 2 well? That's just one so you put the one up top and multiply it out and put whatever the result is at the bottom So what we got is 2 goes into 2 once so 2 times 1 is 2 and you're gonna subtract them That's where the negative comes from so 2 minus 2 is going to be 0 What we're gonna do now is bring the 7 down So how many times does to go into 7 well that's gonna go three times right so you're gonna put the 3 up top there And you're gonna multiply it out and put the the result down here so 3 times 2 is gonna be 6 So 3 times 2 is gonna be 6 and you're gonna put the minus sign there because you're subtracting so 7 minus 6 is gonna be 1 now 2 doesn't go into 1 and what you could do if you're looking for decimals You put a decimal after the 3 and then start adding zeros and continue from there, right? And if you did that you would go you would put a decimal after the 3 so 13 points you would add You can as soon as you add a decimal you can borrow as many zeros as you want and put them back here, right? So what you're gonna do you're not gonna put five or six zeros. You're gonna start out with one zero, right? So what you can do is turn them one Into a 10 and two would go into 10 five times So after the decimal you put a five and then when you did the subtracting out you would get zero so The answer would be 13 and a half, which is what 27 divided by 2 is right? But we're not gonna do that because we want to stay with fractions Especially especially with polynomials. We want to stay with fractions. Okay now 27 divided by 2 you can write You know multiple ways you could say 27 divided by 2 is equal to 13.5, right or 13 and a half So what we got you could write down 27 divided by 2 as 13.5 or you could write down 27 point 27 divided by 2 as 13 and a half, right? 13 so 27 divided by 2 would be 13 and 1 divided by 2, okay So the way you could write it is 27 divided by 2 is equal to 13 plus 1 over 2 which is what we can derive from here, right? 27 27 divided by 2 is going to be 13 Plus 1 divided by 2 by your denominator Now terminology wise in mathematics this guy's called a dividend that guy's called a divisor this guy's called a quotient and one One is called a remainder and again that guy's called a divisor, right? So what you have over here is 27 is your dividend 2 is your divisor 13 is your quotient 1 is your remainder, okay, and this is the terminology that we want to get out of here So you can write down this expression in the following form So you can write this expression 27 divided by 2 is equal to 13 and a half as your Dividend divided by your divisor is equal to your quotient plus your remainder divided by your Divisor right which is exactly what we had over here with a pink right 27 is your dividend 2 is your divisor 13 is your quotient and 1 is your remainder and This guy because we don't like fractions We can multiply both sides of the equation with the divisor with the small d or you can think about it the top guy We can multiply by 2 and that will get rid of our fractions and that's That's the that's the form. We're gonna express our polynomials Okay, that did you can express your polynomials in this form as well But we're gonna express it in the other form which is really called this is also called the division statement Which we're gonna look into a lot further. There's a lot of meaning here, okay, and we will talk about this But keep this in mind. We're just gonna move over and grab another wall and you know expand on this concept