Question

Find a cubic function with the given zeros.

7, -3, 2

Answer 1

\(\bf x=7\implies {\color{blue}{ x-7}}=0\quad x=-3\implies {\color{blue}{ x+3}}=0\quad x=2\implies {\color{blue}{ x-2}}=0\\ \quad \\
(x-7)(x+3)(x-2)=0\implies (x-7)(x+3)(x-2)=\textit{cubic equation}\)

Answer 2

A function \(f(x)\) with zeros \(r_1, r_2, ... r_n\) can be written as \(f(x) = a(x-r_1)(x-r_2)...(x-r_n)\) where \(a\) is an arbitrary constant of your choosing (if needed to fit the curve through a specific point, otherwise use 1).

Answer 3

It's possible that your instructor expects you to fully expand the polynomial, not just give it in factored form. Good multiplication practice, even if not required!