`5)`
`(16x^2 - 22x + 15 -6x^3 + x^4) :(x^2 -2x+3)`
` = [(x^4 - 2x^3 + 3x^2) - (4x^3 - 8x^2 + 12x) + (5x^2 - 10x + 15) ] : (x^2 -2x+3)`
` = [ x^2 (x^2 - 2x+3) - 4x (x^2 -2x+3) + 5 (x^2 -2x+3)] : (x^2-2x+3)`
`= (x^2 - 4x+5)(x^2 - 2x+3)`
`= x^2 - 4x+5`
`6)`
`(6x + 2x^3 - 5 - 11x^2) : (-x +2x^2 +1)`
` = [ (2x^3 - x^2 +x) - (10x^2 - 5x + 5)] : (2x^2-x+1)`
`= [ x (2x^2 - x+1) - 5 (2x^2-x+1)] : (2x^2-x+1)`
` = (x-5)(2x^2-x+1) : (2x^2-x+1)`
` = x-5`
`7)`
`(2x^4 - 3x^3 + 4x^2+1) :(x^2-1)`
`= [ (2x^4 - 2x^2) - (3x^3 - 3x) + (6x^2 - 6) +(7-3x)] : (x^2-1)`
` = [ 2x^2 (x^2-1) - 3x (x^2 - 1) + 6 (x^2 - 1) + (7-3x)] : (x^2 -1)`
` = [ (2x^2 - 3x+6)(x^2 -1) + (7-3x)] : (x^2 -1)`
` = (2x^2-3x+6)(x^2-1) : (x^2 - 1) + (7-3x)/(x^2-1)`
`= 2x^2 - 3x + 6 + (7-3x)/(x^2 - 1)`
`8)`
`(2x^4 + x^3 - 3x^2 - 5x-2) : (x^2-x-1)`
` = [ (2x^4 + 3x^3 + 2x^2) - (2x^3 + 3x^2 +2x) - (2x^2 + 3x+2)] : (x^2 -x-1)`
`= [ x^2 (2x^2 +3x+2) - x (2x^2+3x+2) - (2x^2+3x+2)] : (x^2-x-1)`
` = (x^2 - x-1)(2x^2 + 3x +2) :(x^2-x-1)`
` = 2x^2 +3x+2`
