Difference between revisions of "2010 AMC 12B Problems/Problem 21"

Revision as of 17:22, 12 July 2010

Let $a > 0$ , and let $P(x)$ be a polynomial with integer coefficients such that

$P(1) = P(3) = P(5) = P(7) = a$ , and
$P(2) = P(4) = P(6) = P(8) = -a$ .

What is the smallest possible value of $a$ ?

$\textbf{(A)}\ 105 \qquad \textbf{(B)}\ 315 \qquad \textbf{(C)}\ 945 \qquad \textbf{(D)}\ 7! \qquad \textbf{(E)}\ 8!$

2010 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 20	Followed by Problem 22
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

Revision as of 17:21, 12 July 2010 (view source) Lg5293 (talk \| contribs) (Created page with '== Problem 21 == Let <math>a > 0</math>, and let <math>P(x)</math> be a polynomial with integer coefficients such that <center> <math>P(1) = P(3) = P(5) = P(7) = a</math>, and<b…')		Revision as of 17:22, 12 July 2010 (view source) Lg5293 (talk \| contribs) Newer edit →
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	== See also ==		== See also ==
−	{{AMC12 box\|year=2010\|num-b=12\|num-a=14\|ab=B}}	+	{{AMC12 box\|year=2010\|num-b=20\|num-a=22\|ab=B}}