Art of Problem Solving

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1983 AHSME Problems/Problem 6

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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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