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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).
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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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