Find a Polynomial

Question

Find a polynomial function with the zeros -3,2,4 whose graph passes through the point (7,450)

Answer 1

P(x) = k(x+3)(x-2)(x-4)

(7,450) ---> x = 7 when y = 450, and vice versa

450 = f(7)

450 = k(10)(5)(3)

45- = 150k

k=3

P(x) = 3(x+3)(x-2)(x-4)

= 3(x^2 +x - 6)(x-4)

= 3(x^3 + x^2 - 6x - 4x^2 - 4x + 24)

= 3(x^3 - 3x^2 - 10x + 24)

= 3x^3 - 9x^2 - 30x + 72