Suppose $g(x)$ is a polynomial of degree five for which $g(1) = 2$, $g(2) = 3$, $g(3) = 4$, $g(4) = 5$, $g(5) = 6$, and $g(6) = -113$. Find $g(0)$.
+26367 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, and g(6) = -113.
Find g(0).
\(\begin{array}{rcll} \mathbf{g(0)} &=& \dfrac{ \begin{array}{|rrrrrr|} ~1 & 1 & 1 & 1 & 1 & 2 ~ \\ ~2^5& 2^4& 2^3& 2^2& 2& 3 ~ \\ ~3^5& 3^4& 3^3& 3^2& 3& 4 ~ \\ ~4^5& 4^4& 4^3& 4^2& 4& 5 ~ \\ ~5^5& 5^4& 5^3& 5^2& 5& 6 ~ \\ ~6^5& 6^4& 6^3& 6^2& 6&-113 ~ \\ \end{array} }{ \begin{array}{|rrrrrr|} ~1 & 1 & 1 & 1 & 1 & 1 ~ \\ ~2^5& 2^4& 2^3& 2^2& 2& 1 ~ \\ ~3^5& 3^4& 3^3& 3^2& 3& 1 ~ \\ ~4^5& 4^4& 4^3& 4^2& 4& 1 ~ \\ ~5^5& 5^4& 5^3& 5^2& 5& 1 ~ \\ ~6^5& 6^4& 6^3& 6^2& 6& 1 ~ \\ \end{array} } = \dfrac{-4181760}{-34560} = \mathbf{121} \\ \end{array}\)
