[tex]\text{Polinomul se descompune in factori asa:}\\
6x^5+18x^4+57x^4+171x^3+193x^3+579x^2+276x^2+828x+140x+\\ +420=\\ =6x^4(x+3)+57x^3(x+3)+193x^2(x+3)+276x(x+3)+140(x+3)\\
=(x+3)(6x^4+57x^3+193x^2+276x+140)\\
\text{Acum hai sa descompunem si a doua paranteza:}\\
6x^4+57x^3+193x^2+276x+140=\\
6x^4+12x^3+45x^3+90x^2+103x^2+206x+70x+140=\\
6x^3(x+2)+45x^2(x+3)+103x(x+2)+70(x+2)=\\
(x+2)(6x^3+45x^2+103x+70)\\
\text{Nu are rost sa descompunem mai departe.}\\
\text{Prin urmare raspunsul este:}[/tex]
[tex]\boxed{(x+2)(x+3)(6x^3+45x^2+103x+70)}[/tex]