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Division Algorithm for a Polynomial

If the polyno...

Question

If the polynomial $(x^{4} + 2 x^{3} + 8 x^{2} + 12 x + 18)$ is divided by another polynomial $(x^{2} + 5)$ , the remainder comes out to be $(p x + q)$ , find the values of p and q.

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Solution

Remainder = $2 x + 3$

i.e., $p x + q = 2 x + 3$

$∴ p = 2, q = 3$

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