Difference between revisions of "2014 AMC 12B Problems/Problem 16"
Kevin38017 (talk | contribs) (Created page with "==Problem== Let <math>P</math> be a cubic polynomial with <math>P(0) = k</math>, <math>P(1) = 2k</math>, and <math>P(-1) = 3k</math>. What is <math>P(2) + P(-2)</math> ? <math...") |
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Multiplying the third equation by <math>4</math> and adding <math>2k</math> gives us our desired result, so | Multiplying the third equation by <math>4</math> and adding <math>2k</math> gives us our desired result, so | ||
<cmath>P(2)+P(-2)=12k+2k=\boxed{\textbf{(E)}\ 14k}</cmath> | <cmath>P(2)+P(-2)=12k+2k=\boxed{\textbf{(E)}\ 14k}</cmath> | ||
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Revision as of 21:37, 20 February 2014
Problem
Let be a cubic polynomial with , , and . What is ?
$\textbf{(A)}\ 0\qquad\textbf{(B)}\ k\qquad\textbf{(C)}\ 6k\qquad\textbf{(D)}}\ 7k\qquad\textbf{(E)}\ 14k$ (Error compiling LaTeX. Unknown error_msg)
Solution
Let . Plugging in for , we find , and plugging in and for , we obtain the following equations: Adding these two equations together, we get If we plug in and in for , we find that Multiplying the third equation by and adding gives us our desired result, so