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

To determine whether the binomial can be factored completely, you need to check if it fits into any special factoring patterns. For example, if the binomial is of the form \(a^2 - b^2\), it can be factored into \((a - b)(a + b)\). However, if there are no common factors and it doesn’t fit any patterns, the polynomial may be prime. Keep an eye out for coefficients or terms that could share a common factor, or structures like the difference of squares, which can open doors to factorization magic! If you find that no such patterns or factors exist, congratulations, you've officially met a prime polynomial!