Question

What polynomial has roots of -6, 1, and 4?

Answer 1

If a polynomial has roots of -6, 1, and 4,
Then
x = -6
x = 1
x = 4

Move everything to the left to get
x + 6 = 0
x - 1 = 0
x - 4 = 0

Notice that x + 6, x - 1, x - 4 are factors of the polynomial

By zero product property
(x + 6)(x - 1)(x - 4) = 0

And f(x) = (x + 6)(x - 1)(x - 4)

Expand the RHS to express the cubic poly in standard form.