Question

Rozłoż podane wielomiany na czynniki metoda grupowania
w(x)=x³-3x+2

Answer 1

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