Question

using only algebra find a cubic function with the given zeros. 3,-4,6

Answer 1

Consider the quadratic
x^2 - x - 2

Its roots are 2 and -1. That means we can write it as

x^2 - x - 2 = (x-2)(x+1)

Conversely if I had asked you:
"What is the quadratic with roots 2 and -1?"
you could have written down immediately that it has a factorization:
(x-2)(x+1)

Multiplying that back out, you would find it is x^2 - x - 2

So now for you equation, you have the three roots, so you can write down immediately its factorization.

Answer 2

start with
\[(x-3)(x+4)(x-6)=0\] and then multiply out