`a) (x^3-3x^2+x-3):(x-3)`
`=[x^2(x-3)+(x-3)]:(x-3)`
`=(x-3)(x^2+1):(x-3)`
`=x^2+1`
`b) (6x^3-7x^2-x+2):(2x+1)`
`=(6x^3+3x^2-10^2-5x+4x+2):(2x+1)`
`=[3x^2(2x+1)-5x(2x+1)+2(2x+1)]:(2x+1)`
`=(2x+1)(3x^2-5x+2):(2x+1)`
`=3x^2-5x+2`
`c) (x^4-x^3+x^2+3x):(x^2-2x+3)`
`=(x^4-2x^3+3x^2+x^3-2x^2+3x):(x^2-2x+3)`
`=[x^2(x^2-2x+3)+x(x^2-2x+3)]:(x^2-2x+3)`
`=(x^2-2x+3)(x^2+x):(x^2-2x+3)`
`=x^2+x`
`d) (x^4+x^2+1):(x^2-x+1)`
`=(x^4-x^3+x^2+x^3-x^2+x+x^2-x+1):(x^2-x+1)`
`=[x^2(x^2-x+1)+x(x^2-x+1)+(x^2-x+1)]:(x^2-x+1)`
`=(x^2-x+1)(x^2+x+1):(x^2-x+1)`
`=x^2+x+1`
