# Find P(2013)

1. Sep 6, 2014

### Ratanak

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

2. Sep 6, 2014

### HallsofIvy

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 $P(x)= ax^2+ bx+ c$. 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)?

Do you see a pattern? Can you show that this pattern is correct?