Răspuns :
Observam ca x este factor comun.
Il extragem si obtinem, [tex]x ( x^{2} - 7x + 12)[/tex].
Calculam [tex]\Delta = 7^{2} - 4 * 12 * 1 = 1 [/tex].
Calculam [tex]x _{1} = \frac{7 + 1}{2} = 4 [/tex] si [tex]x _{2} = \frac{7 - 1}{2} = 3 [/tex].
Deci, putem descompune in [tex]x(x-4)(x-3)[/tex].
Il extragem si obtinem, [tex]x ( x^{2} - 7x + 12)[/tex].
Calculam [tex]\Delta = 7^{2} - 4 * 12 * 1 = 1 [/tex].
Calculam [tex]x _{1} = \frac{7 + 1}{2} = 4 [/tex] si [tex]x _{2} = \frac{7 - 1}{2} = 3 [/tex].
Deci, putem descompune in [tex]x(x-4)(x-3)[/tex].
x^3-7x^2+12x=x(x^2-7x+12)=x(x^2-3x-4x+12)=x[x(x-3)-4(x-3)]=x(x-3)(x-4)