Question

descompunere in produs de paranteze

6x^5+75x^4+364x^3+855x^2+968x+420=0

Answer 1

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

$\boxed{(x+2)(x+3)(6x^3+45x^2+103x+70)}$