Find a polynomial of degree 3 knowing it's zeros. (Read description for specific question.)

Question

Find a polynomial of degree 3 with integer coefficients, zeros of 1, -2, and 3, and for which the coefficient of the x^2 term is 3. Expand the polynomial to eliminate parenthesis and to combine like terms. Show all the steps.

Answer 1

The factors of the polynomial are:

 

(x - 1)(x + 2)(x - 3)

(x² + x - 2)(x - 3)

x³ - 2x² - 5x + 6

 

I have no idea as to how to make the coefficient x² to be 3, or even if it should be.