Разложите ** множители : а). x^3-8x^2-2x+16 б). a^3-a^2-4a+4 в). ac^4-c^3+ac^2-c г)....

Question

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

Answer 1

A) =x²(x -8) -2(x -8) =
= (x-8)(x²-2)

b) =a²(a -1) -4(a -1) =
=(a -1)(a² -4)=(a-1)(a-1)(a+1)

в) =c^3(ac -1) + c(ac -1) =
=(ac -1)(c^3 +c)=c(ac-1)(c²+1)

г) =(x²y+x^4)-xy(x²+y)=
=x²(y +x²) - xy(y +x²) =
=(y +x²)(x² -xy)=x(y+x²)(x-y)

Answer 2

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)