Rozłóż wielomiany na czynniki:

1. W(x)=[tex]2x^{3}[/tex]+[tex]8x^{2}[/tex]-10x

2. U(x)=[tex]2x^{3}[/tex]-[tex]x^{2}[/tex]-32x+16

3. V(x)=[tex]2x^{4}[/tex]+54x


Odpowiedź :

1.

W(x)=2x³+8x²-10x=2x(x²+8x-5)=2x(x+4+√21)(x-4+√21)

x²+8x-5=0

Δ=8²-4·1·(-5)=64+20=84 , √Δ=√84=2√21

x1=(-8-2√21)/2

x1=-4-√21

x2=(-8+2√21)/2

x2=-4+√21

x²+8x-5=(x-(-4-√21))(x+(-4+√21))=(x+4+√21)(x-4+√21)

2.

W(x)=2x³-x²-32x+16=x²(2x-1)-16(2x-1)=(2x-1)(x²-16)=(2x-1)(x+4)(x-4)

3.

W(x)=2x^4+54x=2x(x³+27)=2x(x+3)(x²-3x+9)