Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: Beyond Simple Factoring
The reverse FOIL method works perfectly when the leading coefficient (a) equals 1. But what happens when a ≠ 1? For example, how do we factor 2x² - 5x - 3?
This lesson introduces techniques for factoring quadratic expressions where the coefficient of x² is not 1.
The Challenge
When a = 1, the pattern was straightforward:
x² + bx + c = (x + m)(x + n) where m + n = b and m × n = c
When a ≠ 1, the factoring becomes more complex because the first terms of the binomials must multiply to a, not just x².
Adjusting the Pattern
For ax² + bx + c (a ≠ 1), we need two numbers that satisfy:
- Sum: m + n = b
- Product: m × n = a × c