A Polynomial that Passes through the following four points? I'm trying to do this for practice but I'm just going nowhere with it, I'd love to see some work and answers on it.
Thanks :)
Find a polynomial that passes through the points (-2,-1), (-1,7), (2,-5), (3,-1). Present the answer in standard form.
What I've tried:



$$f(x) = a x^3 + b x^2 + c x + d$$
\begin{eqnarray*} 
-1 &=& a (-2)^3 + b(-2)^2 + c(-2) + d \\
 7 &=& a (-1)^3 + b(-1)^2 + c(-1) + d \\
-5 &=& a(2)^3 + b (2)^2 + c (2) + d \\
-1 &=& a(3)^3 + b(3)^2 + c (3) + d
\end{eqnarray*}
or 
\begin{eqnarray*} 
-8 a  + 4b -2c + d &=&  -1\\
-{\ }a{\ } +{\ } b -{\ } c + d &=&{\ } 7 \\
 8a + 4b  + 2c  + d&=&-5 \\
27a + 9b + 3c + d&=&-1
\end{eqnarray*}
with solution
\begin{eqnarray*} 
a&=&{\ }{\ }1\\
b&=&-2\\
c&=&-5\\
d&=&{\ }{\ }5
\end{eqnarray*}
and so $f(x) = x^3 -2x^2-5x+5$
