# How To: Factor a trinomial, find the GCF, then group

This lesson describes the method to find the factors of a trinomial, which consists of three terms, by grouping. First of all, factor out the greatest common factor (GCF), and write the reduced trinomial in parentheses. Let the terms of the trinomial be written in order of exponent of the variable. For example, 3(3X2+2X-8) trinomial is written in the order of variable, with 3(GCF) factored out. Now identify the coefficient of the first and last terms, for example in this case, it is 3 and 8. Now choose a pair of factors whose product is equivalent to the product of first and last terms of the trinomial, and the sum is equal to the middle term, both in terms of value and sign. Rewrite the trinomial by breaking the middle term in terms of the two chosen factors, that is, 3X2 + 6x-4x _8. Now pull out the common factors for each pair ensuring that in both the pairs, we have same monomial in the parentheses. For example, our trinomial will look like X(3X-4)+2(3X-4). Rewrite the trinomial in terms of GCF and the paired factors we get 3(3X-4)(X+2). Hence, we can find the factors of a trinomial by following the four steps viz., find the GCF, find the factors, rewrite the statement and factor by grouping.

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