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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


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    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?
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