What polynomial equation of the least degree has -2,-2,3, and 3 as four of its roots?

f(x) = - 2x³ - 11x² + 12x + 36

Step-by-step explanation:

given that x = a and x = b are the roots of a polynomial then

(x - a) and (x - b) are it's factors and the polynomial is the product of the factors

here x = -2 ( repeated ) and x = 3 (repeated), hence the factors are

(x + 2)² and (x - 3)² → the square denotes a repeated root

f(x) = (x + 2)²(x - 3)² ← expand factors and simplify

     = (x² + 4x + 4)(x² - 6x +9)

     = - 2x³ - 11x² + 12x + 36 ← is a possible equation

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.