Find a degree 3 polynomial having zeros 3 2 and 6 and the co

Find a degree 3 polynomial having zeros -3, 2 and 6 and the coefficient of x^3 equal 1. The polynomial is

Solution : zeros = -3, 2, 6.

The polynomial is

(x+3)(x-2)(x-6)

=(x^2-2x+3x-6)(x-6)

=(x^2+x-6)(x-6)

=x^3+x^2-6x-6x^2-6x+36

=x^3-5x^2-12x+36. Ans