Proof & Structures: Showing n≤0 for Prime/Composite Number

[johnny009]

Hi There,

My apologies, there was an error...in a previous question, which I POSTED ....last week.

This question has now been withdrawn, & replaced with the following :

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a) Show that if n ≤ 0, then n^2 - 14n + 40 is a composite number.

b) Determine, with explanation, all integer values of 'n' for which ...n^2 -14n + 40 is prime

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any guidance on these issues.....will be fantastic!

Thanks a lot.

John

 

[Opalg]

a) show that if n ≤ 0, then n^2 - 14n + 40 is a composite number.

b) Determine, with explanation, all integer values of 'n' for which ...n^2 -14n + 40 is prime

Hint: Factorise the quadratic expression $n^2 - 14n + 40.$

 

[Opalg]

If you have factorised $n^2 - 14n + 40$, then the only cases where this could represent a prime would be when one of the factors is $\pm1$ and the other factor is (plus or minus) a prime. Which values of $n$ give rise to those possibilities?