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Video instructions and help with filling out and completing Fill Form 8815 Div

Instructions and Help about Fill Form 8815 Div

Okay in this video I want to do an example of what's called synthetic division and synthetic division is when you basically are dividing one polynomial by a first-degree polynomial so X to the first it may or may not have you know a number in there if it's just X you would just break things up individually and it'd be pretty easy anyway so suppose we want to divide again X cubed minus 2x squared plus 3x minus 4 we're gonna divide that by X minus 2 what you do in this case is whatever we're dividing by so notice there's a minus 2 it's X minus 2 we actually take the opposite sign and we'll use positive 2 and that's what you stick outside and then notice I have 1x cubed minus 2x squared plus 3x minus 4 notice there's no two terms missing it starts the third degree second degree first degree and then we just have a number all we do is we write the coefficients so one there's a negative 2 in front of the x squared there's a positive 3 in front of the X and there's a negative 4 just hang it out and with synthetic division what you do is the first term you just drop it right down there's nothing to do and then the idea is we multiply so I'm going to take positive 2 times 1 and then stick that number in the next spot so it says positive 2 times 1 will give us positive 2 and then what we do is we add those numbers together in this column so negative 2 plus 2 is going to give me and then we repeat this process now we take positive 2 multiply it by and that's what we stick in the next column so it's as positive 2 times is just going to give us so if we add those together we'll get positive 3 and then again I take positive 2 times positive 3 let me erase my little red dots here we'll take positive 2 times positive 3 they don't give me positive 6 we add the columns together and we get the number 2 this last number is going to be your remainder remaining spelled correctly here and what it says is in summary it says we can actually sew the numbers on the bottom or what are important ok so it says we can actually rewrite X cubed minus 2x squared plus 3x minus 4 divided by X minus 2 so I'm going to keep my numbers at the bottom it says we can actually write that as ok so the highest power was X cubed make things one degree less so this is going to go with my x squared term this is going to go with my X term this is going to be my constant and again the other parts my remainder it says we can actually write x cubed minus 2x squared plus 3x minus 4 divided by X minus 2 as 1x squared plus 0x so usually 0x we'll just leave that out so I'm going to erase it so 1x squared plus 3 and then my remainder is 2 and we put that over whatever we were originally dividing by which is X minus 2 and now we have broken up our original fraction into something a little bit a little bit more simple okay so this would be your solution after you did the synthetic division okay so a useful little trick one other thing I want to point out about synthetic division notice if we look at the thing on top if I call that f of X so if I say f of X equals x cubed minus 2x squared plus 3x minus 4 suppose I wanted to evaluate this suppose I wanted to plug in the number 2 well it turns out if you plug in the number 2 if you do the synthetic division with X minus 2 if you do that synthetic division it says whatever the remainder is that's actually going to be the solution when you plug that value in so just a coincidence here that I plugged 2 in and got 2 out but notice if I plug 2 in I'll get 2 cubed minus 2 times 2 squared plus 3 times 2 minus 4 so this is 8 minus 8 plus 6 minus 4 well the 8 and the 8 cancel out positive 6 minus 4 is a positive 2 okay so synthetic division is actually also a way to evaluate polynomials that remainder again is going to be your solution and sometimes if you have a real tedious problem using synthetic division can be useful for example if you're plugging things into a calculator typically I don't use it really hardly ever but that's just a personal preference of mine so alright I hope this example makes some sense all I think I'm going to do one other one as well just to kind of reinforce this stuff so if you have any questions just send me an email.

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