Explanation:
We can use long division to divide the polynomial (4x³ - 6x² - 4x + 8) by the binomial (2x - 1).
2x² + 2x - 4
2x - 1 | 4x³ - 6x² - 4x + 8
- (4x³ - 2x²)
---------------
-4x² - 4x
+ ( -4x² + 2x )
--------------
-2x + 8
- (-2x + 1)
----------
7
Therefore, the quotient is 2x² + 2x - 4, and the remainder is 7.