Factor the biniomial completely. Select "Prime" if the polynomial cannot be factored.

To factor the binomial completely, first look for common factors. If the binomial is of the form \( ax + b \), with \( a \) and \( b \) being integers, you want to see if there's a greatest common factor (GCF) for both terms. If the terms don't share common factors besides 1 and can't be rewritten in the form of a difference of squares, perfect squares, or other recognizable forms, then it might be prime. For example, \( 6x + 9 \) can be factored as \( 3(2x + 3) \). However, \( x^2 + 2x + 1 \) is fully factored as \( (x + 1)(x + 1) \) or \( (x + 1)^2 \). If no such factors exist, then categorize the binomial as "Prime."