Using the factorised trinomial (4n-7))
, prove that there are only two values of n for which 
is a prime number.
Answers
Answer 1
Answer:
4n² - 15n + 14 is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.
Case n - 2 = 1
That would be n = 3
Then 4n² - 15n + 14 = 5 , which is prime.
Case n - 2 = -1
That would be n = 1
Then 4n² - 15n + 14 = 3, which is also prime.
Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime
Case 4n-7 = -1
That would be n = 3/2 which is not integer, so 4n² - 15n + 14 will not be interger.
For any other n values, 4n² - 15n + 14 will be composite number since it is product of two factors.
Therefore we are left with n = 1 and n = 3; only two values of n.
Case n - 2 = 1
That would be n = 3
Then 4n² - 15n + 14 = 5 , which is prime.
Case n - 2 = -1
That would be n = 1
Then 4n² - 15n + 14 = 3, which is also prime.
Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime
Case 4n-7 = -1
That would be n = 3/2 which is not integer, so 4n² - 15n + 14 will not be interger.
For any other n values, 4n² - 15n + 14 will be composite number since it is product of two factors.
Therefore we are left with n = 1 and n = 3; only two values of n.
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12 feet times 12=144 inches
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it cannot pass through it is too high
1 foot=12 inches
12 feet times 12=144 inches
144+5=149 inches
160>149
it cannot pass through it is too high
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plus you go to OHDLEA?
plus you go to OHDLEA?