Zadanie 1
a)
[tex]3(x+2)-5x(3x+1)=3x+6-15x^2-5x=\boxed{-15x^2-2x+6}[/tex]
b)
[tex](k+1)^2+(k-3)^2=k^2+2k+1+k^2-6k+9=\boxed{2k^2-4k+10}[/tex]
c)
[tex](x^2+4x-1)(x+3)-(x+1)^3=\\\\=x^3+3x^2+4x^2+12x-x-3-(x^3+3x^2+3x+1)=\\\\=x^3+7x^2+11x-3-x^3-3x^2-3x-1=\\\\=\boxed{4x^2+8x-4}[/tex]
Zadanie 2
a)
[tex]x^3+2x^2-x-2=x^2(x+2)-(x+2)=\\\\=(x+2)(x^2-1)=\boxed{(x+2)(x+1)(x-1)}[/tex]
b)
[tex]x^3-6x^2+12x-8=\boxed{(x-2)^3}[/tex]
c)
[tex]x^4+2x^3+x^2=x^2(x^2+2x+1)=\boxed{x^2(x+1)^2}[/tex]
d)
[tex]x^3-4x=x(x^2-4)=\boxed{x(x+2)(x-2)}[/tex]
e)
[tex]x^4-5x^2+4=x^4-x^2-4x^2+4=x^2(x^2-1)-4(x^2-1)=\\\\=(x^2-1)(x^2-4)=\boxed{(x+1)(x-1)(x+2)(x-2)}[/tex]
