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1. How many cubic polynomials f(x) are there such that f(x) has nonnegative integer coefficients and f(1) = 9?

 

2. How many ordered quadruples (a,b,c,d) satisfy, a + b + c + d = 18,
where a,b,c,d are integers such that |a|, |b|, |c|, |d| are each at most 10?

 May 16, 2020
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1. By stars and bars, the number of such polynomials is c(13,3) = 286.

 

2. By stars and bars, the number of solutions is c(26,4) = 14950.

 May 17, 2020

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