Objective: Factor trinomials of the type ax2 + bx + c.
Trinomials of the type ax2 + bx + c (in which a > 1) can be factored using a "trial and error" process that is similar to the process used for trinomials in which a = 1. Instead of merely seeking factors of c that have a sum of b, however, we must also consider factors of a and test them in combination with the factors of c until the process of binomial multiplication results in the correct trinomial.
In order to be efficient when factoring by trial and error, it is important to keep work organized and make educated guesses based on the particular trinomial to be factored. This will limit the time spent in checking unlikely possibilities. To see some simple examples of this process, watch the video below.
In more complex problems, when a and c each have several possible factorizations, the number of options which can be tested increases significantly. In such cases, the presence or absence of a factor which is common to all terms is an extremely helpful piece of information that will reduce the number of possibilities. To see some more complicated examples of the trial and error process, watch the video below.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.