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IRISSAK [1]
3 years ago
14

Find all integers n for which n^2+6n-27 is a prime number? Please tell me how you did it.

Mathematics
1 answer:
taurus [48]3 years ago
5 0
n^2+6n-27=\\
n^2-3n+9n-27=\\
n(n-3)+9(n-3)=\\
(n+9)(n-3)
For the above product to be a prime number, one of the factors must be a prime number and the other must be equal to 1.

n+9=1\\
n=-8\\\\
-8-3=-11
The first factor is equal 1 for n=-8, but the other is euqal -11, which is not a prime number.

n-3=1\\
n=4\\\\
4+9=13
The second factor is equal 1 for n=4 and the first factor is equal 13, which is a prime number.

So, n^2+6n-27 is a prime number for n=4


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