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Question

If the polynomial (x4 + 2x3 + 8x2 + 12x + 18) is divided by another polynomial (x2 + 5), the remainder comes out to be (px + q). Find the values of p and q.

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Solution

Let f(x) = x4 + 2x3 + 8x2 + 12x + 18

It is given that when f(x) is divisible by x2 + 5, the remainder comes out to be px + q.



On division, we get the quotient x2 + 2x + 3 and the remainder 2x + 3.

Since, the remainder comes out to be px + q.

Therefore, p = 2 and q = 3.

Hence, the values of p and q are 2 and 3 respectively.

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