Identify monomials you can factor out of a polynomial by breaking down each term in the polynomial into its smallest component parts. For example, 2x^3 - 8x^2 + 8x can be broken down as such: 2*x*x*x - 2*2*2*x*x + 2*2*2*x.
Determine if the terms have a monomial in common. If they do, this is the monomial factor. In the above example, each term of the polynomial has the monomial factor, 2x, in common.
Factor the monomial out of the polynomial that all of its terms have in common. In the example, 2x is factored out of the polynomial, and the function now reads: 2x(x^2 - 4x + 4).
Solve the now simplified polynomial by setting the function equal to zero in order to find its roots. In the example, 2x(x^2 - 4x + 4) = 0 can be further simplified to 2x(x - 2)(x - 2) = 0. The solution to the polynomial is x = 0 and x = 2.