Question

Find a polynomial function of degree 3 with -2, 2, 5 as zeros.

Answer 1

If -2, 2, and 5 are zeroes then

x = 2
x = -2
x = 5

Move everything to the left. Then
x - 2 = 0
x + 2 = 0
x - 5 = 0

By zero product property
(x - 2)(x + 2)(x - 5) = 0

Expand the left side to form a cubic polynomial, then set it equal to f(x).