Question

Proszę o rozwiązanie .

Answer 1

Zad. treningowe
a)x^3-2x=x(x^2-2)=x(x-pierw z 2)(x+pierw z 2)
b)(x^3-27)=x^3-3^3=(x-3)(x^2+3x+9)
c)x^4-16=(x^2-4)(x^2+4)=(x-2)(x+2)(x^2+4)
d)49x^4-81=(7x^2-9)(7x^2+9)=(x pierw z 7-3)(x pierw z 7+3)(7x^2+9)
e)x^3-x^2-x+1=x^2(x-1)-1(x-1)=(x^2-1)(x-1)=(x-1)(x+1)(x-1)=(x-1)^2(x+1)
f)3x^3-2x^2-6x+4=x^2(3x-2)-2(3x-2)=(x^2-2)(3x-2)=(x -pierw z 2)(x+pierw z 2)(3x-2)
g)x^5-9x^3-x^2+9=x^3(x^2-9)-1(x^2-9)=(x^3-1)(x^2-9)=(x-1)(x^2-x+1)(x-3)(x+3)
h)x^5-x^4-x+1=x^4(x-1)-1(x-1)=(x^4-1)(x-1)=(x^2-1)(x^2+1)(x-1)=(x-1)(x+1)(x^2+1)(x-1)=
(x-1)^2 (x^2+1)(x+1)

Zad. utrwalajace
a)5x-x^3=x(5x-x^2)=x(x pierw z 5-x)(x pierw z 5+x)
b)1+8x^3=1^3+8x^(1+8x)(1+8x+64x^2)
c)81-16x^4=(9-4x^2)(9+4x^2)=(3-2x)(3+2x)(9+4x^2)
d)16-25x^4=(4-5x^2)(4+5x^2)=(2-x pierw z 5)(2+x pierw z 5)(4+5x^2)
e)x^3+x^2-x-1=x^2(x+1)-1(x+1)=(x^2-1)(x+1)=(x-1)(x+1)(x+1)=(x+1)^2 (x-1)
f)2x^3-3x^2-6x+9=x^2(2x-3)-3(2x-3)=(x^2-3)(2x-3)=(x-pierw z 3)(x+pierw z 3)(2x-3)
g)x^5+3x^3-8x^2-24=x^3(x^2+3)-8(x^2+3)(x^3-8)(x^2+3)=(x-2)(x^2+2x+4)(x^2+3)
h) -x^5-x^4+x+1= -x^4(x+1)+1(x+1)=(-x^4+1)(x+1)=-(x^4-1)(x+1)=-(x^2-1)(x^2+1)(x+1)=
-(x-1)(x+1)(x^2+1)(x+1)= -(x+1)^2 (x^2+1)(x-1)