Answer
$2(x+3)(x-2)^2$ or $2x^3-2x^2-16x+24$
Work Step by Step
Step 1. Identify the zeros as $x=-3$ and $x=2$ (multiplicity 2)
Step 2. Write a general form of the equation as $f(x)=a(x+3)(x-2)^2$
Step 3. Use the condition $f(0)=24$, we have $f(0)=a(0+3)(0-2)^2=24$, thus $a=2$
Step 4. Thus $f(x)=2(x+3)(x-2)^2=2x^3-2x^2-16x+24$
