Divisibility in Polynomial
How many natural number are there such that
divides ?
The answer is 2.
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1 solution
since x is divisible by x^3 + x^2 +x + 3 this implies that............ (x^3 +x^2 + x +3) / x is an integer. And (x^3 +x^2 + x +3) / x = ((x^3+x^2 + x ) / x ) + (3/x). Therefore, ((x^3+x^2 + x ) / x ) + (3/x) is an integer if x = 3. And also x = 1 because all integers are divisible by 1. Therefore, they have 2 solution in this problem.