Difference between revisions of "2010 AMC 10B Problems/Problem 25"
(Created page with 'P(x)-a=(x-1)(x-3)(x-5)(x-7)Q(x). Then, plugging in values of 2,4,6,8, we get -2a=-15Q(2)=9Q(4)=-15Q(6)=105Q(8). Thus, the least value of a must be the lcm(15,9,15,105). Solving,…') |
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Revision as of 22:14, 5 April 2010
P(x)-a=(x-1)(x-3)(x-5)(x-7)Q(x). Then, plugging in values of 2,4,6,8, we get -2a=-15Q(2)=9Q(4)=-15Q(6)=105Q(8). Thus, the least value of a must be the lcm(15,9,15,105). Solving, we receive 315, so a=15.
