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Current time:0:00Total duration:3:20

Video transcript

divide x squared minus 3x plus 2 divided by X minus 2 so we're going to divide this into that and we could do this really the same way that you first learn long division so we have X minus 2 being divided into x squared minus 3x plus 2 another way we could have written the same exact expression is x squared minus 3x plus 2 all of that over X minus 2 that that and that are all equivalent expressions now to do this type of long division we can call it algebraic long division you want to look at the highest degree term on the x minus 2 and the highest degree term on the x squared minus 3x plus 2 and here's the X and here's the x squared X goes into x squared how many times or x squared divided by X is what well that's just equal to X so X goes into x squared x times I'm going to write it in this column right here above all of the X terms and then we want to multiply x times X minus 2 that gives us x times X is x squared x times negative 2 is negative 2x and just like you first learned in long division you want to subtract this from that so you want to subtract this from that but that's completely the same as adding the opposite or multiplying each of these terms by negative 1 and then adding so let's multiply that times negative 1 and negative 2 x times negative 1 is positive 2x and now let's add x squared minus x squared those cancel out negative 3x plus 2x that is negative x and then we can bring down this 2 over here so it's negative x plus 2 left over when we only go x times so then we take an X minus 2 going to negative x plus 2 well X goes into negative x negative 1 times negative 1 you could look at it right here negative x divided by X is negative 1 these guys cancel out those guys cancel out so negative 1 times X minus 2 you have negative 1 times X which is negative x negative 1 times negative 2 is positive 2 and we want to subtract this from that just like you do in long division but that's the same thing as multiplying the opposite or multiplying each of these terms by negative one and then adding so negative x times negative one is positive x positive two times negative one is a positive 2 times negative 1 is negative 2 these guys cancel out add up to 0 these guys set up to 0 we have no remainder so we got this as being equal to X X minus 1 and we can verify it if we multiply X minus 1 times X minus 2 we should get this so let's actually do that so if we let's multiply X minus 1 times X minus 2 so let's multiply negative 2 times negative 1 that gives us positive 2 negative 2 times X that's negative 2x let's multiply x times negative 1 that is negative x and then x times X is x squared and then add all the like terms x squared negative 2x minus X that's negative 3x and then 2 plus nothing is just 2 and so we got that polynomial again