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

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

Which polynomial should be added to x^2 -5x+3 to get the polynomial 2x^2 +3x-5 ?

Without expanding, find the value of: (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

Find the value of the polynomial 2x^4 - x^3 + 3x^2 - 5 when x = 0 , x = -1 and x = -2 .

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

Which polynomial is to be substracted from x^2+13x=7 to get the polynomial 3x^2+5x-4 ?