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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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7y ago

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