Problem: is to be factored into prime binomial factors and without a numerical monomial factor. This can be done if the value ascribed to is:
Answer Choices:
A. any odd number
B. some odd number
C. any even number
D. some even number
E. zero
Solution:
Let the factors be and . Then
. Since is odd, all its factors are odd. Therefore each of the numbers and is odd. The same is true for and . Since the product of two odd numbers is odd, and are odd numbers; , the sum of two odd numbers, is even.