Wat is the factorization of 2x^4+3x^3-38x^2-27x+180=0
You know any rational roots have numerator that divides 180, and denominator that divides 2.
That's a lot of choices, but expect some easy ones to pop up.
A little synthetic division reveals that we have
f(x) = (x-3)(x+3)(x+4)(2x-5)