Разложите на множители :
а). x^3-8x^2-2x+16
б). a^3-a^2-4a+4
в). ac^4-c^3+ac^2-c
г). x^2y-x^3y+X^4-xy^2
а). x^3-8x^2-2x+16
б). a^3-a^2-4a+4
в). ac^4-c^3+ac^2-c
г). x^2y-x^3y+X^4-xy^2
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1)xˇ3-8xˇ2-2x+16=xˇ2(x-8)-2(x-8)=(x-8)(xˇ2-2)2)aˇ3-aˇ2-4a+4=aˇ2(a-1)-4(a-1)=(a-1)(aˇ2-4)=(a-1)(a+2)(a-2)
3)acˇ4-cˇ3+acˇ2-c=cˇ3(ac-1) +c(ac-1)=
=(ac-1)(cˇ3+c)=c.(cˇ2+1)(ac-1)
4)xˇ2y-xˇ3y+xˇ4-xyˇ2=xˇ2y-xyˇ2-xˇ3y+xˇ4=
=xy(x-y)+xˇ3(x-y)=(x-y)(xy+xˇ3)=x.(y+xˇ2)(x-y)