1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find P(2013)

  1. Sep 6, 2014 #1
    P(x) is polynomial of degree 2012, P(k)=2^k, k=0,1,....,2012. Find P(2013)
     
  2. jcsd
  3. Sep 6, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Start by looking at simpler versions:

    Suppose P is polynomial of degree 2, P(0)= 1, P(1)= 2, P(2)= 4. Since P is of degree 2 we can write it as [itex]P(x)= ax^2+ bx+ c[/itex]. Use P(0)= 1, P(1)= 2, P(2)= 4 to find a, b, and c. What is P(3)?

    Suppose P(x) is a polynomial of degree 3, P(0)= 1, P(1)= 2, P(2)= 4, P(3)= 8. Since P is of degree 3, [itex]P(x)= ax^3+ bx^3+ cx+ d[/itex] use the values at x= 0, 1, 2, and 3 to find a, b, c, and d. What is P(4)?

    Do you see a pattern? Can you show that this pattern is correct?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted