3x⁵ $-$ 4x⁴ + 3x³ + 2x ; x² $-$ 3

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Solution

Here, quotient = 3x³ $-$ 4x² + 12x $-$ 12
and remainder = 38x $-$ 36

$∴ 3 x^{5} - 4 x^{4} + 3 x^{3} + 2 x = (x^{2} - 3) (3 x^{3} - 4 x^{2} + 12 x - 12) + 38 x - 36$

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