Prerequisite knowledge and skills:. Terms to know:.
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For polynomials that have more than three terms, a common technique is factoring by grouping. We group terms together and look for common factors in each group.
Group the first two terms and.
Factor the greatest common factor from each group:. Factor out the binomial common factor:. Why not? Make a table for.
What did you notice? More detailed example.
At first glance, it looks like this expression cannot be factored because nothing can be factored out of the first two terms. If we rearrange the terms, however, factoring becomes possible:.
Rearrange the terms:. Factor the binomial common factor:. The above example shows that rearranging the terms may be necessary before factoring.
Make a table of several such values. Note that a plus sign replaces the minus, but the last two terms are negative. Note that we can still factor further:. What would be the x- intercepts of the graph of? Graph this function on your grapher and make a note of the x -intercepts.
Now graph the original expression on the same set of axes. What do you notice about the two graphs?
The graphs are also here. As before, we can observe what happens when we substitute values for x into each expression. What is the result? Put the original expression into Y1 and the factored expression into Y2 on your graphing calculator. How do the values of the original form compare to those in the factored form?
Will this always happen? A sample table is here. Now factor the remaining expression using grouping. Factor out the GCF, :.
Checkpoint Grouping 1. Example 5.
This time, we group the first three terms together. More Examples of Factoring by Grouping.
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