List all of the possible rational roots.
Use synthetic division to test the possible rational roots until you are able to find a complete factorization.
Provide a final factorization of each polynomial using the roots you found.
p(x) = 3x^4 - 17x^3 + 9x^2 + 41x + 12
p(x) = 2x^3 - 13x^2 + 10x + 25
p(x) = 2x^3 + x^2 - 4x - 3