Need help for this question!

Question

Determine the integer values of n for which n^2-18n+45 is a prime number. 

Answer 1

n^2-18n+45

factor

(n-3)(n-15)

a prime number must be a whole number greater than 1

a prime number can be factored only as 1*p where p is prime

2=1*2

3=1*3

5=1*5

and so on

n-3 must be equal to 1 or n-15 must be equal to 1

n-3=1

n=4

(4-3)(4-15)=1*(-11) but -11 is not greater than 1

n-15=1

n=16

(16-3)(16-15)=13*1=13

n=16 makes n^2-18n+45 a prime number

16^2-18*16+45=256-288+45=13

Answer 2

Hi Amy, to evaluate the expression: n² -18n + 45, replace n with integer values starting at 2 since 2 is the first prime number.

 

n = 2, result is 13, a prime number.

 

n = 3, result is 0.

 

n > 3, results are negative.

 

Answer: n = 2.

 

Questions?