When a ≠ 1
Completion requirements
When a ≠ 1
When \(a \ne 1\), factoring \(ax^2 + bx + c \) is more difficult using inspection. Another method, called Grouping by Decomposition, helps to more consistently determine the factors, although inspection can still be used. If you struggle with factoring, then please focus on Grouping by Decomposition, which will be discussed in the next section.
The key to factoring trinomials of this form (where \(a \) does not equal 1), by inspection, is to focus on the values of \(a \) and \(c \). When factored, the first terms of each binomial multiply to give \(a \) and the last terms of each binomial multiply to give \(c \). Using trial and error, you will try various combinations of factors of \(a \) and \(c \), looking for the combination that works. This can be a bit time consuming.