Question

Aduceti la cea mai usoara forma expresiile:
x³-2x²-5x+6
x³-5x²+7x-3
Va rog!!

Answer 1

Răspuns:

a) x³-2x²-5x+6= x³-x²-x²+x-6x+6=

= x²(x-1)-x(x-1)-6(x-1)=

= (x-1)×(x²-x-6)=

= (x-1)×(x²+2x-3x-6)

= (x-1)×(x+2)×(x-3)

b) x³-5x²+7x-3= x³-x²-4x²+4x+3x-3=

= x²(x-1)-4x(x-1)+3(x-1)=

= (x-1)×(x²-4x+3)=

= (x-1)×(x²-x-3x+3)=

= (x-1)×(x-1)×(x-3)=

= (x-1)²×(x-3)