Polynomial function

Question

Find a third-degree polynomial P(x) that has zeros at x = −2, x = 2, and x = 3,

 and whose x-term has coefficient 16

Answer 1

P(x) = a(x + 2)(x - 2)(x - 3) = a(x² - 4)(x - 3) = a(x³ - 3x²- 4x + 12); - 4a = 16; a = - 4

P(x) = - 4x³ + 12x² + 16x - 48