Find a third-degree polynomial function such that f(0) = 18 and whose zeros are -1, 2, and 3. Using complete sentences, explain how you found it

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anonymous · Answer

This can be solved using a system of equations.$$f(x)=a \times x^{3} + b \times x^{2} + c \times x + d$$$$f(0)=18=a \times 0 + b \times 0 + c \times 0 + d$$$$f(-1)=0=a \times (-1)^{3} + b \times (-1)^{2} + c \times -1 + d$$$$f(2)=0=a \times 2^{3} + b \times 2^{2} + c \times 2 + d$$$$f(3)=0=a \times 3^{3} + b \times 3^{2}+ c \times 3 + d$$So then your system is$$\left[\begin{matrix}0 & 0 & 0 & 1 & 18 \ -1 & 1 & -1 & 1 & 0 \ 8 & 4 & 2 & 1 & 0 \ 27 & 9 & 3 & 1 & 0\end{matrix}\right]$$So now you can use any method you prefer to solve this system.