Answer
$f(x)=2x^{3}-4x^{2}-22x+24$
Work Step by Step
If $r$ is a real zero of a polynomial function $f$ .
then $(x-r)$ is a factor of $f.$
$f(x)=a(x-(-3))(x-1)(x-4)=a(x+3)(x-1)(x-4)$
We find a by substituting $f(6)=180$
$180=a(6+3)(6-1)(6-4)$
$180=90a$
$a=2$
$f(x)=2(x+3)(x-1)(x-4)$
$f(x)=(2x+6)(x^{2}-5x+4)$
$f(x)=2x^{3}-10x^{2}+8x+6x^{2}-30x+24$
$f(x)=2x^{3}-4x^{2}-22x+24$
