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Polynomials and Rational Functions · Paper 3 — Free Maths AA HL Practice Questions

1ChallengeLAQDivision of polynomialss10 marksPaper 3~15 min
Let f(x)=x3+2x2−5x−6x2−4f(x) = \dfrac{x^3 + 2x^2 - 5x - 6}{x^2 - 4}.
(a)
Show that f(x)f(x) can be written in the form f(x)=Ax+B+Cx+Dx2−4f(x) = Ax + B + \frac{Cx + D}{x^2 - 4} where A,B,C,D∈ZA, B, C, D \in \mathbb{Z}, and state the values of AA, BB, CC, and DD. [4 marks]
(b)
State and justify the equation of the oblique asymptote of the graph of y=f(x)y = f(x). [3 marks]
(c)
Determine whether the graph of y=f(x)y = f(x) intersects its oblique asymptote, and if so, find the coordinates of any such point(s). [3 marks]
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