What could be the factors of $-9m⁴+12m³+14m²-12m-5$

Question

$-9m⁴+12m³+14m²-12m-5$. The question has been asked in iit genius exam of fitjee and is of class 8 level. We have to find all possible roots.

Answer 1

By the rational root theorem we find the rational roots $m=\pm 1,-\frac{1}{3},\frac{5}{3}$, so that $$ -9m^4+12m^3+14m^2-12m-5= - (3m + 1)(3m - 5)(m + 1)(m - 1). $$