Question

Rozłóż wielomian na czynniki:

Answer 1

W(1)=1-2-5+6=0  ⇒ W(x) jest podzielny przez (x-1)

x³-2x²-5x+6= x²(x-1)-x(x-1)-6(x-1)=(x-1)(x²-x-6)=

(x-1)(x²+2x-3x-6) = (x-1)*[x(x+2)-3(x+2)]= (x-1)(x+2)(x-3)
II sposob:
x(x²-2x+1)-6x+6=x*(x-1)²-6(x-1) = (x-1)*[x(x-1)-6]=(x-1)(x²-x-6)=
(x-1)(x+2)(x-3)
Δ=1+4*6=25
x=(1-5)/2=-2  v  x=(1+5)/2=3