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Find an equation of the slant asymptote. Do not sketch the curve.

$ y = \dfrac{4x^3 - 10x^2 - 11x + 1}{x^2 - 3x} $

$y=4 x+2$

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Oregon State University

University of Michigan - Ann Arbor

Idaho State University

So we're gonna, um, do polynomial division to find our slant. As until so how many times x squared go into four x cube? Um, for X And when we multiply for X by each term, we're gonna switch the sign so that the first term cancels out. So four x times x squared is four x cubed. We're gonna make it negative. So for negative for X cubed and then for X times minus three X is negative 12 x But we're gonna make it X squared. We're gonna make it positive. So positive 12 x squared. All right, so the 1st 1 cancel first term cancels out the second term. We're left with two x squared on, then dropped the minus 11 x and the plus one. All right. And now we have to see how many times X squared goes into two x squared. And that is twice so, plus two. So two times x squared. But switches sign. So minus two x squared. Next. Her plus six. Thanks. And then don't forget to drop the one. So first term cancels out. We're left with minus five x plus one. And so the X squared has a higher power than X. So this is a remainder. This is our quotient. And the quotient is our slant s into so are sent as until it is found it four x plus two.