Divide the polynomial 4a^6-5a^4+3a^2-a divided by 2a-1

Using synthetic division with a divisor zero value of 1/2, you get quotient coefficients of 4, 2, - 4, - 2, 2, 0. Dividing those by 2 (the coefficient of "a" in the given denominator), we get a quotient of

... 2x⁵ + x⁴ - 2x³ - x² + x

You will get the same result using long division.