1999 AHSME Problems/Problem 12

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What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions $y \equal{} p(x)$ (Error compiling LaTeX. Unknown error_msg) and $y \equal{} q(x)$ (Error compiling LaTeX. Unknown error_msg), each with leading coefficient $1$?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 8$