# Trinomial Factoring

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A trinomial is an algebraic expression containing three terms, where the terms are separated either by the addition operation or the subtraction operation. Trinomials are also considered as polynomials since they also contain variables and constants written together. In order to simplify a given trinomial, we can use the trinomial factoring method where the trinomial is either reduced from three terms to a single term, or it can be simplified to its lowest terms. With the help of trinomial factoring, the algebraic expressions can be easily simplified and solved to get the answer.

Example 1: Simplify the given trinomial, 12x6 + 18x4 – 30x3using factoring method.

Given trinomial= 12x6 + 18x4 – 30x3

We should first find the greatest common factor of the three numbers 12, 18 and 30 so that it can be factored out!

GCF of 12, 18 and 30 is 6.

Similarly, common factor of x6, x4 and x3 is x3.

Now, pulling out ‘6’ and x3 we get: 6x3 (2x3 + 3x – 5).

Hence the factored answer for the given trinomial is 6x3(2x3 + 3x – 5).

Example 2: Simplify the given trinomial, 20x5 - 50x3 – 80xusing factoring method.

Given trinomial= 20x5 - 50x3 – 80x

We should first find the greatest common factor of the three numbers 20, 50, 80 so that it can be factored out!

GCF of 20, 50 and 80 is 10.

Similarly, common factor of x5, x3 and x is x.

Now, pulling out ‘10’ and x we get: 10x (2x4 –5x2 – 8).

Hence the factored answer for the given trinomial is 10x (2x4 – 5x2 – 8).