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Coefficients (Posted on 2024-08-16)

Let P(x) be a polynomial with non-negative integer coefficients such that P(0)=33, P(1)=40, and P(9)=60000. Find P(2).

No Solution Yet Submitted by Danish Ahmed Khan

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Faster way to determine the polynomial (spoiler)

| Comment 2 of 3 |

The last coefficient is 33

60000 - 33 = 59967

59967 = 101230 (Base 9)

So, P(x) can be x^5 + x^3 + 2x^2 + 3x + 33

And because we know that all the coefficients except the last are non-negative integers less than 9 (in fact, less than or equal to 7), this is the only possible P(x).

Edited on August 16, 2024, 2:39 pm

Posted by Steve Herman on 2024-08-16 14:30:09

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