What must be added to `x^(4)-x^(3)+x^(2)-5x` to get `x^4-x^2+4?`

What must be added to x^(4) -3x^(2) +2x+ 6 to get x^(4) -2x^(3) -x+ 8?

What must be added to x^(4) - x^(3) + x^(2) + x + 3 to obtain x^(4) + x^(2) - 1 ?

What must be added to 2x^(4)-5x^(3)+2x^(2)-x-3 so that the result is exactly divisible by ( x-2 ) ?

What should be added to x^(2)-x^(2) -x+1 to get 5x^(2) -4x^(2) +3x -1 ?

What should be added to x^(2)-x^(2) -x+1 to get 5x^(2) -4x^(2) +3x -1 ?

What must be subtracted from x^(4)+3x^(3)+4x^(2)-3x-6 to get 3x^(3)+4x^(2)-x+3

What must be added to x^(4)+2x^(3)-2x^(2)-2x-1 to obtain a polynomial which is exactly divisible by (x^(2)+2x-3) ?

What must be added to 3x^(2)-5x+7 to obtain 2x^(2)-8x+9 .

What must be added to f(x)=4x^(4)+2x^(3)-2x^(2)+x-1 so that the resulting polynomial is divisible by g(x)=x^(2)+2x-3