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Current time:0:00Total duration:3:24

Dividing polynomials by linear expressions

Video transcript

we're told divide the polynomials the form of your answer should either be just a clean polynomial or some polynomial plus some constant over X plus 2 where P of X is a polynomial and K is an integer fair enough and if we were doing this on Khan Academy as a screenshot from Khan Academy it we would have to type this in but we're just going to do it by hand and like always pause this video and try to do it on your own before we work through it together all right now let's work through it together and what we're trying to do is divide X plus 2 into 3x to the third power plus 4 x squared minus 3x plus 7 and so like always we focus on the highest degree terms first X goes into 3x to the third power how many times 3x squared times we'd want to put that in the second degree column 3x squared 3x squared times 2 is 6x squared 3x squared times X is 3x to the third power there's something very meditative about algebraic long division anyway we want to subtract what we just wrote from what we have up here so let's subtract and these characters cancel out and then 4x squared minus 6x squared is negative 2x squared bring down that negative 3x and now we would want to say hey how many times does X go into negative 2x squared well it would go negative 2x times put that in our first-degree column negative 2x times 2 is negative 4x negative 2x times X is negative 2x squared now we want to subtract what we have here in orange from what we have up here in teal so we either put a negative around the whole thing or we distribute that negative and that becomes a positive that becomes a positive and so this is equal to the x squared terms cancel out negative 3x plus 4x is just going to be a straight-up X bring down that 7x plus 7 how many times does X go into X well one time let me do it use a new color year so how many times does X go into X it goes one time put that in the constant column 1 times 2 is 2 1 times X is X we want to subtract these characters and we're left with 7 minus 2 is 5 and so we can rewrite this whole thing as and we deserve it I guess a little bit of a drumroll 3 x squared minus 2x plus 1 plus the remainder 5 over X plus 2 one way to think about is hey I have this remainder after I'd have to keep dividing it by X plus 2 if I really want to figure out exactly what this is now if I wanted these expressions to be completely identical I would put a condition on the domain that X cannot be equal to negative 2 because if X was equal to negative 2 we'd be dividing by 0 here but for the purposes of this exercise you just have to input you just have to input this part right over here you'd have to type it in which I guess isn't the easiest thing to do in the world but it's worth doing alright see you in the next video