Answer:
4n² + 1
Explanation:
Odd integers are whole numbers that give 1 as a reminder when divided by 2. In other words, odd integers are whole numbers that do not have 2 as a factor.
Adding 1 to an even number would always result in an odd integer but adding 1 to an odd integer would result in an even integer (i.e a number divisible by 2).
From a review of the options given, when n is an odd integer, 4n² + 1, 3n², n² would result in an odd integer, while 3n² + 1 and 4n² would result in an even integer.
When n is an even integer 3n², n², and 4n² would result in an even integer while 4n² + 1 and 3n² + 1 would result in odd integers.
As such, only 4n² + 1 results in an odd integer irrespective of the value of n.