##### Item1.4.4.7.e

Rather than looking for a degree three polynomial, suppose we wanted to find a polynomial that passes through the four points and that has degree four, such as

\begin{equation*} p(x) = a + bx + cx^2 + dx^3 + ex^4 \text{.} \end{equation*}Solve the system of equations for the coefficients. What can you say about the existence and uniqueness of the solutions?