Use a System of Equations to Find the Cubic Function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$

Multiple Choice

Use a system of equations to find the cubic function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ that satisfies given equations. Solve the system using matrices.
$$\begin{aligned}f ( 2 ) & = - 26 \\f ( - 2 ) & = 6 \\f ( 1 ) & = 0 \\f ( - 1 ) & = - 2\end{aligned}$$

A) $a = 2 , b = - 2 , c = 1 , d = - 1$
B) $a = - 26 , b = 6 , c = 0 , d = - 2$
C) $a = - 3 , b = - 3 , c = 4 , d = 2$
D) $a = - 26 , b = 30 , c = - 12 , d = 16$
E) $a = 50,598 , b = - 54,650 c = - 730 , d = 518$