[tex]3x^3+4x^2-3x+2=3x^3+6x^2-2x^2-4x+x+2=3x^2(x+2)-2x(x+2)+1(x+2)=(x+2)(3x^2-2x+1).[/tex]

Verified answer

[tex]\displaystyle\bf\\3x^{3} +4x^{2} -3x+2=3x^{3} +6x^{2} -2x^{2} -4x+x+2=\\\\=\Big(3x^{3} +6x^{2} \Big)-\Big(2x^{2} +4x\Big)+\Big(x+2\Big)=3x^{2} \cdot\Big(x+2\Big)-2x\cdot\Big(x+2\Big)+\Big(x+2\Big)=\\\\=\boxed{\Big(x+2\Big)\Big(3x^{2} -2x+1\Big)}[/tex]