GeoGebra Classroom

# Breaking 'Em Up (2 of 2)

## OBJECTIVE: To learn how to factor Type II General Quadratic Trinomials (a ≠ 1)

In a previous lesson, you learned how to factor Type I General Quadratic Trinomials (a = 1). Breaking 'Em Up (1 of 2): https://www.geogebra.org/m/ns9wnxtf In this lesson, you'll learn how to factor Type II General Quadratic Trinomials (a ≠ 1). As in all factoring problems, the first step is to factor out the Greatest Common Factor (GCF) or the Common Monomial Factor (CMF). If the resulting polynomial has three terms with a coefficient in the x2 term other than 1, the A-C Test may be applied to find out if the polynomial can be factored according to the technique that will be described here. How does the A-C test work? 1. Arrange the quadratic expression in the general form: Ax2 + Bx + C, where A ≠ 1. 2. Factor out the GCF/CMF as in any other problem. 3. Multiply A x C and look for factors of the product AC whose sum is the coefficient of the middle term if AC > 0 or whose difference is the coefficient of the middle term if AC < 0. If such sum or difference exists, the process described in the video below can be used to factor the quadratic trinomial. Watch the video to learn the process.
The applet below can be used to practice factoring Type II General Quadratic Trinomials (a ≠ 1). Solve the problems on a separate sheet, and then verify your answer by clicking "Check Factors."

## Applet by Steve Phelps

Below is a set of problems that require you to factor Type II General Quadratic Trinomials (a ≠ 1). Check the Answer Box below for the correct answers.