How Do You Factor A Hard Trinomial?
This article explains how to use the decomposition method to factor a difficult trinomial. It explains the entire process of breaking up a trinomial (expressed in quadratic form) into two binomials. This will be useful for algebra students in the middle to high school grades. First, we must determine what makes a trinomial “hard” or difficult to factor. One example of a difficult trinomial to factor is one where the coefficient of the quadratic term is not 1 and which cannot be factored into all three terms. For example, let’s look at the trinomial 3×2 + 10x + 8. The coefficient in the quadratic term, 3, is not a common factor of the other two coefficients, 10 and 8. However, we can use a process called the decomposition method to factor this trinomial. We begin by multiplying the first coefficient, 3, by the last coefficient, 8. I will use the symbol * to express multiplication throughout this article. Now, we must look at the coefficient in the middle term of the trinomial, which is
