The image below demonstrates the factoring a fourth degree polynomial with four terms. The first step is to find the greatest common factor (GCF). Factor trees are used here to accomplish this. This technique comes in handy if you cannot come up with the GCF mentally. In the second step, a new binomial appears with its own GCF. We again use factor trees. In the third step, a difference of squares emerges. In the fourth step, the polynomial is completely factored. The next two images demonstrate the simplification of rational expressions. This time, factor trees are used slightly differently, to find the least common multiple (LCM) rather than the GCD (as used for factoring a polynomial expression). Each factor is circled in the tree where it is most numerous. All of the circled numbers are multiplied to yield the LCM, which is the lowest common denominator in the rational expression.
In the last step, we check to see if the trinomial in the numerator is factorable, which turns out it is not.
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Mr. Ken Marciel

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