Разложите квадратный трехчлен на множители:
x^2+x-56
5x^2-18x+16
3x^2-11x-14
x^2-x-1
6x^2+5mx+m^2
(m-n)x^2-nx-m

$1); ; x^2+x-56=(x+7)(x-8)2); ; 5x^2-18x+16=0; ,; ; x_{1,2}=frac{9pm 1}{5}= left [ {{x=frac{8}{5}} atop {x=2}} right. 5x^2-18x+16=5(x-frac{8}{5})(x-2)=(5x-8)(x-2)3); ; 3x^2-11x-14=0; ,; ; x_{1,2}=frac{11pm 17}{6}= left [ {{x=-1} atop {x=frac{14}{3}}} right. 3x^2-11x-14=3(x+1)(x-frac{14}{3})=(x+1)(3x-14)4); ; x^2-x-1=0; ,; x_{1,2}= frac{1pm sqrt5}{2} x^2-x-1=left (x-frac{1-sqrt5}{2}right )left (x-frac{1+sqrt5}{2}right )$

$5); ; 6x^2+5mx+m^2=0D=25m^2-24m^2=m^2x_1=frac{-5m-|m|}{12}= left [ {{-frac{m}{3},; m textless 0} atop {-frac{m}{2},; m geq 0}} right. x_2= frac{-5m+|m|}{12}= left [ {{-frac{m}{2},; m textless 0} atop {-frac{m}{3},; m geq 0}} right. 6x^2+5mx+m^2=6(x-frac{5m+|m|}{12})(x+frac{5m-|m|}{12})=$

$=6(x+frac{m}{2})(x+frac{m}{3})=(2x+m)(3x+m)$

$6); ; (m-n)x^2-nx-m=0D=n^2+4m(m-n)=n^2-4mn+4m^2=(n+2m)^2x_1=frac{n-|n+2m|}{2(m-n)}; ,; ; x_2=frac{n+|n+2m|}{2(m-n)}$

$(m-n)x^2-nx-m=(m-n)(x-frac{n-|n+2m|}{2(m-n)})(x-frac{n+|n+2m|}{2(m-n)})$