Question

Daca x^3+3x^2+2x=(x+a)(x+b)(x+c) atunci a+b+c=....
Am nevoie de rezolvare completa+explicatie

Answer 1

x³+3x²+2x=(x+a)(x+b)(x+c)

x³+3x²+2x=x(x²+3x+2)=x(x²+2x+x+2)=x[x(x+2)+(x+2)]=x(x+2)(x+1)

x(x+2)(x+1)=(x+a)(x+b)(x+c)  ⇒  a+b+c=0+2+1=3

Answer 2

(x+a)(x+b)(x+c)=(x^2+xb+xa+ab)(x+c)=x^3+x^2c+x^2b+xbc+x^2a+xac+xab+abc
=x^3+x^2*(c+b+a)+x(ac+ab+bc)+abc
ca si explicatia
am luat partea dreapta si am inmultit parantezele, am dat factor comun
acum compar ce am obtinut cu ce era in partea stanga si observ ca a+b+c=3 ca si numarul care sta linga x^2