Rozłóż na czynniki: a) 2x³-8x²+5x b) x^4+x³+4x²+3x+3 c) x^4-81

[latex]a) 2x^{3}-8x^{2}+5x= x(2x^{2}-8x+5)=x(x-frac{4-sqrt{6}}{2})(x-frac{4+sqrt{6}}{2})\ ---\ Delta=b^{2}-4ac\ Delta=(-8)^{2}-4*2*5\ Delta=64-40\ Delta=24\ sqrt{Delta}=2sqrt{6}\ \ x_{1}=frac{-b-sqrt{Delta}}{2a}=frac{8-2sqrt{6}}{4}=frac{4-sqrt{6}}{2}\ \ x_{2}=frac{-b+sqrt{Delta}}{2a}=frac{8+2sqrt{6}}{4}=frac{4+sqrt{6}}{2}[/latex] =================================================== [latex]b) x^{4}+x^{3}+4x^{2}+3x+3=\ =x^{4}+x^{3}+x^{2}+3x^{2}+3x+3=\ =x^{2}(x^{2}+x+1)+3(x^{2}+x+1)=\ =(x^{2}+3)(x^{2}+x+1)\ ---\ x^2+3=0\ Delta=b^{2}-4ac\ Delta=0^{2}-4*1*3\ Delta=0-12\ Delta=-12 extless 0\ ---\ x^{2}+x+1=0\ Delta=b^{2}-4ac\ Delta=1^{2}-4*1*1\ Delta=1-4\ Delta=-3 extless 0[/latex] =================================================== [latex]c) x^{4}-81=\ =(x^{2}-9)(x^{2}+9)=\ =(x-3)(x+3)(x^{2}+9)\ ---\ x^{2}+9=0\ Delta=b^{2}-4ac\ Delta=0^{2}-4*1*9\ Delta=0-36\ Delta=-36 extless 0[/latex]