How to Factor Trinomials With a Calculator

By Dan Lecocq
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Many trinomials factor or express as the product of binomials. The AC method is one way to do so and involves factoring by grouping. The FOIL method relies on finding the factors of one of the coefficients that add up to another of the coefficients. When using a calculator, however, you factor a trinomial by using the quadratic equation to determine its roots, which appear directly in the factored result.

Rewrite your trinomial in the format ax^2 + bxy + cy^2, bearing in mind that in most cases, y is a constant leading to the format ax^2 + bx + c. For example, rewrite "3x - 4 + x^2" as "x^2 + 3x - 4" yielding a = 1, b = 3, c = -4.

Calculate the discriminant of your trinomial by squaring b and subtracting 4 * a * c. If this quantity (b^2 - 4 * a * c) is less than zero, then the trinomial cannot be factored as the product of two binomials. Otherwise, proceed to Step 3. For the example, "x^2 + 3x - 4" the discriminant is (b^2 - 4 * a * c) = 9 - 4 * 1 * -4 = 25, which means factoring is possible.

Find the first root of the trinomial by negating b, subtracting the square root of the discriminant you determined in Step 2, and dividing that difference by 2a. For the example "x^2 + 3x - 4," that is -b - sqrt(b^2 - 4ac) / 2a = (-3 - 5) / 2 = -4. This means that when x = -4, the example trinomial takes on the value 0.

Find the second root of the trinomial as you did in Step 3, but this time negate b, add the square root of the discriminant and divide the sum by 2a. For the example "x^2 + 3x - 4," that is -b + sqrt(b^2 - 4ac) / 2a = (-3 + 5) / 2 = 1. This means that when x = 1, the example trinomial takes on the value 0.

Write the trinomial as the product of x minus the first root times x minus the second root: (x - root1)*(x - root2). For the example with roots -4 and 1, this means that x^2 + 3x - 4 = (x - 1)(x + 4).

About the Author

Based in Denver, Dan Lecocq has been writing computer-related articles since 2011. He brings with him a wealth of expertise in graphics, general programming and mathematics. Lecocq received a Bachelor of Science in computer science from the Colorado School of Mines and a Master of Science in applied mathematics from King Abdullah University.