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,…')
 
(Redirected page to 2010 AMC 12B Problems/Problem 21)
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P(x)-a=(x-1)(x-3)(x-5)(x-7)Q(x).
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#REDIRECT [[2010 AMC 12B Problems/Problem 21]]
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.
 

Latest revision as of 15:26, 17 June 2020