To get the polynomial function,
Given the roots (-4, -2, 3)
The general equation will be
[tex]y=A(x+4)(x+2)(x-3)[/tex]
Since we are told that it passes through the point (2, -6)
Then, this means that x=2, y = -6
We will then substitute the values to get A
[tex]-6=A(2+4)(2+2)(2-3)[/tex]
=>
[tex]-6=A(6)(4)(-1)[/tex]
=>
[tex]-6=-24A[/tex]
=>
[tex]A=-\frac{6}{-24}=\frac{1}{4}[/tex]
=>
[tex]A=\frac{1}{4}[/tex]
Therefore, the polynomial function is
[tex]y=\frac{1}{4}(x+4)(x+2)(x-3)[/tex]
On simplifying further, we will obtain
[tex]y=\frac{1}{4}(x^3+3x^2-10x-24)[/tex]
