Divide $3 x^{4} + 2 x^{2} - 3$ by $(x + 1)$ and find quotient and remainder.

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Solution

We, know that

$P (x) = g (x) . Q (x) + R (x)$

$⟹ 3 x^{4} + 2 x^{2} - 3 = (x + 1) (3 x^{3} - 3 x^{2} + 5 x - 5) + 2$

Hence, Quotient $Q (x) = 3 x^{3} - 3 x^{2} + 5 x - 5$

And, Remainder $= 2$

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