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Do the long division by removing the highest power of x at each stage:
_________________2x_+_6
_______---------------------
_2x-1_|_4x²_+_10x_-_4
_________4x²_-___2x
_________-------------
_________________12x_-_4
_________________12x_-_6
_________________----------
________________________2
→ (4x² + 10x - 4) ÷ (2x - 1) = 2x + 6 remainder 2.
Checking:
(2x + 6)(2x - 1) + 2 = 4x² -2x + 12x - 6 + 2 = 4x² + 10x - 4 = dividend.
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