Transcript

Hello, Tom from everystepcalculus.com and everystepphysics.com. Long division problem regarding functions you know in calculus if it comes up in calculus whatever, index 8 to get to my menu your going to change long division and your going to enter your function, you have to press alpha before you enter anything in these functions here I’ve already entered the problem so I’m going to press cause it’s a long problem and it takes time save time and you notice this is called the dividend (x^4-9*x^3+25*x^2-8*x-2) and this is called the divisor (x^2-2) you set it up just like a regular numerical long division problem, this off to the left if the screen was wider I could do that for you but I can’t so I have to do it this way and remember your dividing x ^2 into x ^4 first getting the answer of x ^2 and your multiplying x ^2*x^2 which is x^4 and then your going to multiple x^2*-2 which gets -2x^2and your going to change the signs because your subtracting from this so I’ll show you how to do that but remember that this is a divisor we’re operating dividing this into several things that come along here okay so it always give you a chance to change incase you’ve made a mistake but I’ll say it’s okay now here we’ve divided the divisor x^2 into x^4 and you get x^2 and you multiple that times it and then change the sign -x^4 we multiple x^2*-2 and we get -2x^2 and we change the sign to make it +2x^2 okay and then we add them, you notice now that we have 25x^2 up here we’ll if the screen was wider we would have -8x over here and -2 over here but I have to bring it down to show you that it’s still there okay but we are going to deal with this one and this one and this plus this is 27 and this of course becomes 0 so we have 0+(27*x^2) and we bring down the (-26*x)+(-2) okay we are going to divide x^2 into 27*x^2 and we are going to get 27 and we change the sign, write this all on your paper exactly as you see it and you have to keep the coulomb’s of x^2 and x and x^3 all together okay now 27*-2 because a minus -18*x okay -18x-8x is 26x-26x and we still have to bring down the -2 okay and we of course multiple that to come up with a minus which negates these two here and then when we multiple the minus 2 times the minus 27 we get -54 and that change its sign and become 54 okay and 54-2 here becomes 52 so we get 52 we got -2x now once in long division the divisor cannot be divided into this anymore this all becomes as one then you divide that by the divisor so we have [(-26*x)+(52)]/(x^2-2) here is the answer (x^2)+(-9*x)+(27)+[(-26*x)+(52)]/(x^2-2) complicated you have to do it on paper and you will see where it’s much clearer I have trouble explaining it here because of such a small screen and it’s all crammed into one but all the answer is correct and you will get all the problems are correct. Pretty neat hah everystepcalculus.com go to my site buy my programs and pass your calculus, have a good one.

## Long Division, (x^4+3*x^3-4*x^2+5*x+7)/(x^3-3)

Transcript

Hello everyone this is Tom from everystepcalculus.com and everystepphysics.com. This video is about long division of functions of a function I’m going to make others also, lets get started index 8 to get to my menu I’m already at long division to save time as you scroll down the menu and we are going to enter our problem you have to press alpha before you enter anything in these entry lines in my programs okay and the problem is alpha (x^4+3*x^3-4*x^2+5*x+7)/(x^3-3) press enter now it’s showing you what you have entered and you can change it if you want now notice that this is the divisor (x^3-3)and this is the is the dividend (x^4+3*x^3-4*x^2+5*x+7) here and there is not really any words for this line here the divisor line whatever it’s not hieratical sign if we had a larger screen than the titanium i would have the all just as a regular long division that we use in regular numbers, numeric long division but this is functions okay so remember this x^3-3 her now we are going to divide that first into x^4 it’s loading here when it says busy and once you’ve loaded it its very fast from then own in your programs so notice that equals x and x times x^3 is x ^4 and we have to change the sign to subtracting so subtract this an then x times a minus 3 is 3x -3x and then we change the sign to 3x okay now again if the screen was longer I would have 5x plus 7 right up here and you want to keep your answers for the, this is called a quotient up here this is a quotient and you want to keep these In there coulomb’s like this is in the x to the 4 Coulomb’s so minus this and it’s going to be zero and this is in the x coulomb’s 3x so you want to make sure this is still there don’t forget that yet and the next screen that equals zero and we pull down the 3x^3 and the minus x squared and then we add the X’s together which is 8x+7 so now x^3 into 3 x^3 which is 3 which we should you in quotient above and curses 3x 3 and when we subtract it we get zero of course here zero we pull down the -4*x^2 and the 8*x above and then we are adding this you notice that the 3 * the minus 3 and the divisor is minus 9 and we change the sign to make it a plus 9 so we get 16 now any time this is below the powers of devisers you are all done with long division in this okay so this is the answer, I’ll show you the answer here, here is the answer (x)+(3)+ [(-4*x^2)+(16)]/(x^3-3). Pretty neat hah everystepcalculus.com go to my site buy my programs and pass your calculus curse, do your homework etc. Have a good one.