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1983 AHSME Problems/Problem 6

Revision as of 12:01, 7 June 2016 by Katzrockso (talk | contribs) (Created page with "== Problem 6 == When <math>x^5, x+\frac{1}{x}</math> and <math>1+\frac{2}{x} + \frac{3}{x^2}</math> are multiplied, the product is a polynomial of degree. <math>\textbf{(A)}...")
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Problem 6

When $x^5, x+\frac{1}{x}$ and $1+\frac{2}{x} + \frac{3}{x^2}$ are multiplied, the product is a polynomial of degree.

$\textbf{(A)}\ 2\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 6\qquad \textbf{(D)}\ 7\qquad \textbf{(E)}\ 8$

Solution

$x^5(x+\frac{1}{x})\implies (x^6+\frac{1}{x^4})(1+\frac{2}{x}+\frac{3}{x^2})\implies x^6+J(x)$, so $6, \fbox{C}$

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