Assuming you want to divide 4x^3 + 0x^2 - 3x + 4 by 2x - 5 using polynomial long division:
2x^2 + 4x + 7
---------------------
2x - 5 | 4x^3 + 0x^2 - 3x + 4
- (4x^3 - 10x^2)
---------------
10x^2 - 3x
- (10x^2 - 25x)
---------------
22x + 4
Therefore, the quotient is 2x^2 + 4x + 7 and the remainder is 22x + 4.
Thus, we can write:
4x^3 + 0x^2 - 3x + 4 = (2x - 5)(2x^2 + 4x + 7) + (22x + 4)
So the division of the polynomial 4x^3 + 0x^2 - 3x + 4 by 2x - 5 results in the quotient 2x^2 + 4x + 7 and the remainder 22x + 4.