(6x^3 +19x^2 +19x+6):(3x+2)=

((6x^3+6)+(19x^2+19x)):(3x+2)=

(6(x^3+1)+19x(x+1)):(3x+2)=

(6(x+1)(x^2-x+1)+19x(x+1)):(3x+2)=

(((x+1)(6(x^2-x+1)+19x)):(3x+2)=

(x+1)(6x^2-6x+6+19x):(3x+2)=

(x+1)(6x^2+13x+6):(3x+2)=

(x+1)*6*(x+2/3)(x+3/2):(3(x+2/3)=

2(x+1)(x+3/2)=

(x+1)(2x+3)

Verified answer

(6x3+19x2+19x+6)=2x(в квадрате только х)+5х+3