question_answer

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

Answer:

Remainder \[=2x+3\]

i.e.,                   \[px+q=2x+3\]

\[\therefore p=2,\,q=3\]