Our strategy will aim to factor the polynomial as much as possible: once completely factored, the polynomial will become a multiplication of polynomials of lower degree:
and its zeroes will be the ones of its factors.
Since the polynomial has no constant term, you can factor it as follows:
To continue, we must factor the quadratic expression in the parenthesis. A common way to factor expressions like is to find the two solutions and and write the polynomial as .
To find the solutions, we can use the quadratic formula
and since in our case , the solving formula becomes
So, the two solutions are and and we write the polynomial as .
So, the complete factorization is
So, the zeroes of the cubic polynomial we started with are the zeroes of the three polynomials in the factorization: yields a solution for , yields a solution for and yields a solution for .