Recall that the general form of a third-degree polynomial is:
[tex]g(x)=k(x-a)(x-b)(x-c),[/tex]where k is a constant, and a, b, and c are the zeros of the polynomial.
Therefore:
[tex]p(x)=k(x+3)(x+2)(x-1).[/tex]Now, to determine the value of k, we consider the y-intercept:
[tex]p(0)=-14=k(0+3)(0+2)(0-1).[/tex]Solving for k, we get:
[tex]\begin{gathered} -14=-6k, \\ k=-\frac{14}{-6}, \\ k=\frac{14}{6}, \\ k=\frac{7}{3}. \end{gathered}[/tex]Finally:
[tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]