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