Calculating P(2013) of Polynomial P(x) of Degree 2012

[Ratanak]

P(x) is polynomial of degree 2012, P(k)=2^k, k=0,1,...,2012. Find P(2013)

 

[HallsofIvy]

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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 P(x)= ax^2+ bx+ c. 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, P(x)= ax^3+ bx^3+ cx+ d use the values at x= 0, 1, 2, and 3 to find a, b, c, and d. What is P(4)?

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