Rozkład na czynniki

[gnomek89]

Czy ktoś moze wie jak rozlozyc te wielomiany na czynnyki?
a) 9\(\displaystyle{ x^{4}}\)+\(\displaystyle{ x^{3}}\)+\(\displaystyle{ x^{2}}\)=

b) \(\displaystyle{ x^{3}}\)-3x-2= wskazówka -3x=-x-2x

c) \(\displaystyle{ x^{5}}\)-\(\displaystyle{ x^{4}}\)-5\(\displaystyle{ x^{3}}\)+5\(\displaystyle{ x^{2}}\)+6x-6=

[wb]

a)
\(\displaystyle{ 9x^4+x^3+x^2=x^2(9x^2+x+1)}\)

[ Dodano: 28 Października 2007, 09:52 ]
b)
\(\displaystyle{ x^3-3x-2=x^2-4x+x-2=x(x^2-4)+(x-2)= \\ =x(x-2)(x+2)+(x-2)=(x-2)(x(x+2)+1)= \\ =(x-2)(x^2+2x+1)=(x-2)(x+1)^2}\)

[soku11]

c)
\(\displaystyle{ x^5-x^4-5x^3+5x^2+6x-6=
x^4(x-1)-5x^2(x-1)+6(x-1)=
(x-1)(x^4-5x^2+6)\\
x^2=t\\
t^2-5t+6=0\\
\Delta=25-24=1\\
t_1=2\quad t_2=3\\
(t-2)(t-3)=0\\
(x-1)(x^2-2)(x^2-3)=0\\
(x-1)(x-\sqrt{2})(x+\sqrt{2})(x-\sqrt{3})(x+\sqrt{3})\\}\)

POZDRO