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Suppose \(g(x)\) is a polynomial of degree five for which \(g(1) = 2, g(2) = 3, g(3) = 4, g(4) = 5, g(5) = 6, g(6) = -113\) . Find g(0).

 Dec 22, 2019
 #1
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We can use a difference table on the values of the polynomials: https://brilliant.org/wiki/method-of-differences/

 

So the first differences are 1, 1, 1, 1, -119.  The second differences are 0, 0, 0, -120.

 

If we continue, we find that g(0) = -17.

 Dec 23, 2019
 #2
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I agree with #1 that a difference table is the way to go, I don't see how to use the remainder theorem, but I get g(0) = 121.

 Dec 23, 2019

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