How do you factor x^3-6x^2-x+30?

Refer to explanation

Explanation:

We check using Rational Root theorem if any of the divisors of 30 are roots of the equation.

In our case $- 2 , 3 , 5$ are roots of the equation hence the polynomial is factored as

${x}^{3} - 6 {x}^{2} - x + 30 = \left(x + 2\right) \left(x - 3\right) \left(x - 5\right)$