9514 1404 393
Answer:
32
Step-by-step 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
