How to Factor out Trinomials

By Nicole Harms
Hilde Vanstraelen

Factoring out trinomials refers to doing the opposite of the FOIL Method. When you do the FOIL Method on a set of parentheses, like (x + 7) (x + 8), you get a trinomial as a result, which in this case is x^2 +15x + 56. Factoring trinomials involves breaking the trinomial down into its basic factors. This is one of the fundamental skills of any Algebra classroom, so take the time to learn it well!

Look at each term to determine if there is a common factor, and if there is, factor it out of the trinomial. If you are factoring 6x^6 + 30x^5 + 36x^4, you can factor out a common factor of 6x^4, which leaves you with 6x^4 (x^2 +5x +6).

Factor the trinomial by writing out all of the possible factors of the last term, provided there is no coefficient in front of the x^2 term, and then figure out which two factors will add together to make the coefficient of the second term. These will be the numbers used in the two binomials. In this example, the factors of 6 are 2 * 3 and 1 * 6, and the pair that adds together to make 5 is 2 and 3, so the answer is 6x^4 (x + 3)(X + 2).

Factor using the guess and check method if there is a coefficient in front of the x^2 term, such as in 3x^2 + 7x + 4.

Start by writing out all of the factors of the coefficients of the first and last terms. In this example, the factors of 3 are 3 * 1, and the factors of 4 are 1 * 4 and 2 * 2.

Make combinations using these factors, then check them using the FOIL Method to determine if they make the original trinomial. For instance, you could try (1x + 4) (3x +1), but this gives you 3x^2 + 13x +4, which is not correct.

Continue trying combinations of factors until you find the right one. You will find that (1x + 1) (3x +4) gives you 3x^2 + 7x +4, so this is the answer.

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