Szczegółowe wyjaśnienie:
a) W(x) = x³ - 4x² + 2x + 3
W(x) = x³-3x² - x²+3x - x+3
W(x) = x²(x-3) -x(x-3) -1(x-3)
W(x) = (x² - x - 1)(x-3) Δ=1²-4·1·(-1) √Δ = √5 > 0
[tex]x_{1} =\frac{1-\sqrt{5} }{2}[/tex] [tex]x_{2} =\frac{1+\sqrt{5} }{2}[/tex]
W(x) = (x - [tex]\frac{1-\sqrt{5} }{2}[/tex])(x - [tex]\frac{1+\sqrt{5} }{2}[/tex])(x-3)
b) W(x) = x³ - 4x² + 2x - 8
W(x) = x²(x-4) + 2(x - 4)
W(x) = (x²+2)(x-4) Δ=0²-4·1·2 Δ = -8 < 0
W(x) = (x²+2)(x-4)
