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Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3). - ICSE Class 10 - Mathematics

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Question

Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).

Solution

Let the required number be k.
Let f(x) = x2 + x + 3 + k
It is given that f(x) is divisible by (x + 3).
∴  Remainder = 0
f (-3) = 0
(-3)2 + (-3) + 3 + k = 0
9 – 3 + 3 + k = 0
9 + k = 0
k = -9
Thus, the required number is -9.

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Solution Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3). Concept: Remainder Theorem.
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