`a,x^4-2x^3+2x-1`
`=x^4-x^3-x^3+x^2-x^2+x+x-1`
`=x^3(x-1)-x^2(x-1)-x(x-1)+(x-1)`
`=(x-1)(x^3-x^2-x+1)`
`=(x-1)[x^2(x-1)-(x-1)]`
`=(x-1)(x-1)(x^2-1)`
`=(x-1)^2(x-1)(x+1)`
`=(x-1)^3(x+1)`
`b,a^6-a^4+2a^3+2a^2`
`=a^2(a^4-a^2+2a+2)`
`=a^2[a^2(a^2-1)+2(a+1)]`
`=a^2[a^2(a-1)(a+1)+2(a+1)]`
`=a^2(a+1)[a^2(a-1)+2]`
`=a^2(a+1)(a^3-a^2+2)`
`=a^2(a+1)[a^3+a^2-2a^2+2a-2a+2]`
`=a^2(a+1)[a^2(a+1)-2a(a+1)-2(a+1)]`
`=a^2(a+1)(a+1)(a^2-2a-2)`
`=a^2(a+1)^2(a^2-2a-2)`
`c,x^4+x^3+2x^2+x+1`
`=x^4+x^2+x^3+x+x^2+1`
`=x^2(x^2+1)+x(x^2+1)+(x^2+1)`
`=(x^2+1)(x^2+x+1)`
`d,x^4+2x^3+2x^2+2x+1`
`=x^4+x^3+x^3+x^2+x^2+x+x+1`
`=x^3(x+1)+x^2(x+1)+x(x+1)+(x+1)`
`=(x+1)(x^3+x^2+x+1)`
`=(x+1)[x^2(x+1)+(x+1)]`
`=(x+1)(x+1)(x^2+1)`
`=(x+1)^2(x^2+1)`
`e,x^2y+xy^2+x^2z+y^2z+2xyz`
`=x^2y+x^2z+xy^2+y^2z+2xyz`
`=(x^2y+x^2z+xyz)+(xy^2+y^2z+xyz)`
`=x(xy+xz+yz)+y(xy+yz+xz)`
`=(x+y)(xy+xz+yz)`
`f,x^5+x^4+x^3+x^2+x+1`
`=x^4(x+1)+x^2(x+1)+(x+1)`
`=(x+1)(x^4+x^2+1)`
