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

A classic example of factoring a binomial is the expression \(x^2 - 9\). This can be figured out using the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\). Here, \(x^2\) is \(a^2\) with \(a = x\), and \(9\) is \(b^2\) with \(b = 3\). Therefore, \(x^2 - 9\) factors to \((x - 3)(x + 3)\). On the flip side, if you have a binomial like \(2x + 3\), you cannot factor it further since there are no common factors and it doesn't fit the difference or sum of squares framework. Thus, it would be designated as "Prime." Remember, recognizing when you're done factoring is as important as the factoring itself!