Rozłóż wielomian na czynniki. a) x3 - 1/2x2 + 4x -2 ( to co przy 1/2x to kwadrat ) b) -12x3 + 4x2 + 9x -3 c) 5x5 + 2x4 + 10x3 + 4x2 Z góry dzięki !!

[latex]a) x^{3}-frac{1}{2}x^{2}+4x-2=x^{2}(x-frac{1}{2})+4(x-frac{1}{2})=(x^{2}+4)(x-frac{1}{2})\ -----\ \ b) -12x^{3}+4x^{2}+9x-3=-12x^{3}+9x+4x^{2}-3=-12x(x^{2}-frac{3}{4})+4(x^{2}-frac{3}{4})=\ \ =(4-12x)(x^{2}-frac{3}{4})=-12(x-frac{1}{3})(x-frac{sqrt{3}}{2})(x+frac{sqrt{3}}{2})\ -----\ \ c) 5x^{5}+2x^{4}+10x^{3}+4x^{2}=x^{2}(5x^{3}+2x^{2}+10x+4)=x^{2}[x^{2}(5x+2)+2(5x+2)]=\ \ =x^{2}(x^{2}+2)(5x+2)=5x^{2}(x^{2}+2)(x+frac{2}{5})[/latex]

a) ...=x^2(x-1/2)+4(x-1/2)=(x-1/2)(x^2+4) b) ...=-4x^2(3x-1)+3(3x-1)=(3x-1)(-4x^2+3)=[latex](3x-1)(sqrt{3}-2x)(sqrt{3}+2x)[/latex] c) ...=x^4(5x+2)+2x^2(5x+2)=(5x+2)(x^4+2x^2)=(5x+2)x^2(x^2+2)