Question

Descompuneti in factori:
a) x³-6x²+11x-6
b) x³-3x+2
c) x³-x-6

Answer 1

a) x³-3x²-3x²+9x+2x-6 = x²(x-3) -3x(x-3)+2 (x-3)=
     = (x-3)*(x²-3x+2) = (x-3)*(x-2)*(x-1)
     x²-3x+2 = x²-2x-x+2 = x(x-2) -(x-2)= (x-2)*(x-1)
b)x³-4x+x+2= x(x²-4)+ (x+2) = x(x-2)(x+2) + (x+2) = (x+2) [x(x-2) +1]=
  = (x+2)*(x²-2x+1)= (x+2) * (x-1)²
c) x³-4x+3x-6 = x(x²-4) +3(x-2) = x(x-2)(x+2)+ 3(x-2)= (x-2) [x(x+2)+3] = 
   = (x-2) (x²+2x+3)