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Question
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
Solution
Let the number k be added and the resulting polynomial be f(x).
So, f(x) = 3x3 – 5x2 + 6x + k
It is given that when f(x) is divided by (x – 3), the remainder is 8.
∴ f(3) = 8
3(3)3 – 5(3)2 + 6(3) + k = 8
81 – 45 + 18 + k = 8
54 + k = 8
k = – 46
Thus, the required number is – 46.
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