rozłóż wielomian na czynniki jak najniższych stopni x2+x-6 x2-7x+10 2x2+5x-3 x2-6x-7 x3+6x-7

[latex]x^{2}+x-6=x^{2}+3x-2x-6=x(x+3)-2(x+3)=(x-2)(x+3)[/latex] [latex]x^{2}-7x+10=x^{2}-5x-2x+10=x(x-5)-2(x-5)= \ \ =(x-2)(x-5)[/latex] [latex]2x^{2}+5x-3=2x^{2}+6x-x-3=2x(x+3)-(x+3)= \ \ =(2x-1)(x+3)[/latex] [latex]x^{2}-6x-7=x^{2}-7x+x-7=x(x-7)+(x-7)=(x+1)(x-7)[/latex] [latex]x^{3}+6x-7=x^{3}-x^{2}+x^{2}+7x-x-7= \ \ =x^{2}(x-1)+x(x+7)-(x+7)=x^{2}(x-1)+(x-1)(x+7)= \ \ =(x-1)( underbrace{x^{2}+x+7}_{Delta=1^{2}-4*1*7 extless 0})[/latex]