Interpret terms, factors, and coefficients in polynomial and rational expressions.
Determine rational end behavior from degrees and leading terms
Problem
For \((2x^3~+~1)/(x^2~-~4)\), compare the numerator and denominator degrees and determine the end-behavior asymptote, including any required division.
Big Picture
What this problem is really about
Compare the numerator and denominator degrees before applying an end-behavior rule. When the numerator is exactly one degree higher, polynomial division produces a linear quotient rather than a horizontal level. Rewrite the function as that quotient plus a proper rational remainder; because the remainder approaches zero at both ends, the quotient line controls the asymptotic behavior.
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