[tex]1)\\ \frac{3x+5 }{x^2+3x+2} =\frac{3x+5 }{(x+1)(x+2)} \\\\1.\\ \\x^3+x^2+3x+3=x^2(x+1)+3(x+1)=(x+1)(x^2+3)[/tex]
[tex]2. \\\\x^3-3x^2+4=x^3 -2x^2- x^2+4=x^2(x-2) - (x^2-4)=\\\\=x^2(x-2) - (x -2)(x+2)=(x-2) [x^2 - (x+2) ]=\\\\=(x-2) ( x^2-x-2) =(x-2) ( x^2+x-2x-2)=\\\\=(x-2) [x( x +1)-2(x+1))]= (x-2)( x +1)(x-2)=( x +1)(x-2)^{2}[/tex]
