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 February 19th, 2011, 09:09 AM #1 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 2 Problems [1] Median of 10 numbers is shifted from 6 to 8 when 15 is added. What will the median be if 15 is replaced with 7? [2] $\text{Let p[x]= x^{3}-2x^{2}+3x-4. Find the largest prime factor of P[4]-P[2].}$
 February 19th, 2011, 02:12 PM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: 2 Problems Is (2) not simply asking you to calculate the function value at x = 4 and at x = 2 and find the difference?? You could use synthetic division if you prefer...
February 19th, 2011, 05:01 PM   #3
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Re: 2 Problems

Quote:
 Originally Posted by The Chaz Is (2) not simply asking you to calculate the function value at x = 4 and at x = 2 and find the difference?? You could use synthetic division if you prefer...
You are right, it turns out that for #2, largest prime factor is 19. p[4]-p[2] = 38 = 19*2.
I think I was frustrated with these Olympiad problems that I didn't even care to try some of them.

 February 19th, 2011, 05:07 PM #4 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: 2 Problems For (1), the only possible options are 6, 7, or 8

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