Answer
$4x^3 - 18x^2 + 14x + 12$
Work Step by Step
The question asks for a polynomial that satisfies the conditions stated below.
Degree: 3
Zeros -1/2, 2, 3
Constant: 12
So the zeros are $(x+1/2)(x-2)(x-3)$
The current constant is 1/2 * 2 * 3 = 3; so the polynomial must be multiplied by 4
Thus the polynomial is $4(x+1/2)(x-2)(x-3)$
$(4x + 2)(x^2 - 5x + 6)$
$4x^3 - 18x^2 + 14x + 12$
