
Polynominal
Hey, i read a very interesting exercise in an old mathbook and i really dont know how to solve it..
John and Nancy get homework from their math teacher. John forgets to write the polynomial down. He asks nancy what it is but she doesn't want to tell him right away. She says: for every xvalue you give me i'll give you the yvalue.
John doesnt know the grade of the polynominal and he wants to get it as fast as possible. What's the shortest way and can you prove this?
Can someone solve this or help me solving it?
Thanks

Re: Polynominal
Can't think of anything better than forming a difference table.
Arrange for the x values to be equally spaced.
If the first differences are constant, it's linear. If the second differences are constant it's a quadratic, if the third differences are constant it's a cubic, and so on.

Re: Polynominal
I got it. Just ask the exact value of f(pi).
If you have 3x^2 + 2x + 6
F(pi) = 3pi^2 +2pi +6
It's unpossible that nancy gives him a number because it wouldn't be exact.