Question 286542
Since they are the zeros, then the factors are 
{{{(x-3)}}}
{{{(x-4)}}}
{{{(x+2)}}}
The simplest polynomial would be the product of these three factors,
{{{f(x)=(x-3)(x-4)(x+2)}}}
{{{f(x)=(x^2-7x+12)(x+2)}}}
{{{f(x)=x^3-7x^2+12x+2x^2-14x+24}}}
{{{f(x)=x^3-5x^2-2x+24}}}
I leave it to you to verify that 3, 4, and -2 are still zeros for f(x).