Question 779139
Rational Roots Theorem would seem most useful, but first factor the constant factor of 4.


{{{12x^4-20x^3+4x^2}}}
{{{4(3x^4-5x^3+x^2)}}}
and also factor the common {{{x^2.}}}
{{{highlight(4x^2(3x^2-5x+1))}}}


If the determinant is negative, then you can leave like that, since the quadratic factor may be easiest in the trinomial form.
{{{(-5)^2-4*3*1=25-12=13}}},   POSITIVE 13.


Still could be best to leave it like it is, because the roots of the quadratic are irrational, making the factorization of this quadratic a bit messy looking.