Question

List all of the potential rational zeros of the following polynomials. Then use polynomial division and the quadratic formula, if necessary, to identify the actual zeros.

Answer 1

\[g (x)= x^3-6x^2-5x+30\]

Answer 2

x = 6 is a zero to g by inspection. Then we can factor out
(x - 6)(x^2 - 5) = 0
This is zero whenever:\[x^2 - 5 = 0 \rightarrow x = \pm \sqrt{5}\]So both square roots complete all zeros.
As for the first part, I didn't understand it quite well. Potentially, all rational numbers can be zeros for this polynomial.