Rozloz wielomian na czynniki

Question

A) W(x)= x³-x²+x-1
b) W(x)=x³-2x²-2x+4
c)W(x)=x³-3x²+2x
d)W(x)=x (do szostej) +7x( do piatej)+6x( do czwartej)

Answer 1

a) x³-x²+x-1 = x²(x-1)+1(x-1)= (x²+1)(x-1)
b) x³-2x²-2x+4 = x²(x-2)-2(x-2)= (x²-2)(x-2)
c) x³-3x²+2x = x(x²-3x+2)
    Δ= 1    x1= -2   x2= 1
   x(x²-3x+2)= x(x-1)(x+2)   (zamieniasz znaki bo przenosisz na 2 strone)
d) x^6 + 7x^5 +6x^4 = x^4 (x²+7x+6) = x^4 (x+6)(x+1)
   Δ= 25   x1=-6    x2=-1