Question

Let n be a positive integer. Then the number of common factors of n² + 3n + 1 and n² + 4n + 3 is

• A. n+1
• B. n-1
• C. 2
• D. 1

Answer 1

The correct option is D

1

Two positive integers p and q will have a common factor other than one, only when is a divisor of both p and q. Now, (n² + 4n + 3) - (n² + 3n + 1) = n + 2 and it is a not a factor of n² + 4n + 3 = ( n + 1 ) (n + 3 ) or n² + 3n + 1 = ( n + 1 )² + n. Hence the common factor of n² + 4n + 3 and n² + 3n + 1 is just 1.