Odpowiedź:
[tex]x^4+5x^3+x^2+5x=x(x+5)(1+x^2)\\x^8+x^7-12x^6=x^6(x^2+x-12)=x^6\left(x-3\right)\left(x+4\right)\\x^3+x^2+x=x(\underset{\Delta<0}{x^2+x+1})\\x^3+x^2-6x=x(x^2+x-6)=x\left(x-2\right)\left(x+3\right)\\x^4+4x^3+4x^2=x^2(x^2+4x+4)=x^2\left(x+2\right)^2[/tex]
[tex]x^3+2x^2-4x-8=(x+2)(x^2-4)=(x+2)(x-2)(x+2)=(x+2)^2(x-2)\\x^4+5x^2+6=\left(\underset{\Delta<0}{x^2+2}\right)\left(\underset{\Delta<0}{x^2+3}\right)\\x^3+x^2-4x-4=(x+1)(x^2-4)=(x+1)(x-2)(x+2)\\x^4+x^3+8x^2=x^2(\underset{\Delta<0}{x^2+x+8})[/tex]