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# Factoring Trinomials Using Trial & Error

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In this lesson, we learn how to factor trinomials using trial and error into the product of two binomials when the leading coefficient is not one. For this scenario, the process is much more tedious. We generally can use two different methods: factoring by grouping, or reverse FOIL. In order to factor a trinomial with grouping, we first re-write the trinomial as a four term polynomial. We do this by finding two integers whose product is a • c and whose sum is b. We use those two integers to expand the middle term; we can then use factoring by grouping to attain the product of two binomials. The alternative method uses reverse FOIL. When we use reverse FOIL, we must undo the FOIL process. In most cases, this process is more tedious than using the factoring by grouping method. We will also look at some special case scenarios that require us to factor out the GCF before we begin or factor when two variables are involved.

Factoring Trinomials by Trial & Error:

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