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A polynomial P has non-negative integer coefficients. If P(1) = 8 and P(10) = 2312, what is P(2)?​

User UHMIS
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9514 1404 393

Answer:

32

Explanation:

If coefficients are positive integers, then the polynomial cannot be higher degree than 3. 10^4 = 10,000, so even a coefficient of 1 will give too large a value. P(1) = 8 tells us that the sum of coefficients must be 8, so we cannot have a degree lower than 3.

The sum of digits in 2312 is 8, so it works out that the polynomial is ...

P(x) = 2x^3 +3x^2 +x +2 . . . . matches P(1) = 8 and P(10) = 2312

Then P(2) is ...

P(2) = ((2·2 +3)2 +1)2 +2

P(2) = 32

User Debaditya
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