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Question
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
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Solution
Let the number to be subtracted be k and the resulting polynomial be f(x).
So, f(x) = x3 + 3x2 – 8x + 14 – k
It is given that when f(x) is divided by (x – 2), the remainder is 10.
∴ f(2) = 10
(2)3 + 3(2)2 – 8(2) + 14 – k = 10
8 + 12 – 16 + 14 – k = 10
18 – k = 10
– k = 10 – 18 = – 8
k = 8
Thus, the required number is 8.
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