The polynomial equation is:
[tex]P(x)=a(x+b)(x-c)(x-d)[/tex]We want to find the value of a knowing that the points (-2,0), (1,0), (3, 0) and (0, -18) satisfy the equation.
The three first points are the roots of the polynomial, so we can easily say:
[tex]b=2,c=1,d=3\text{ are the roots of the polynomial}[/tex]Now we can use this values and the last point to find the value of a:
[tex]\begin{gathered} -18=a(0+b)(0-c)(0-d) \\ -18=a\cdot b\cdot c\cdot d=a\cdot2\cdot1\cdot3=6a \\ a=-\frac{18}{6}=-3 \end{gathered}[/tex]