Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: From Multiplication to Factorization
In elementary school, you learned that multiplication and division are inverse operations. If 3 × 5 = 15, then factoring 15 means reversing the operation to find 3 and 5. The same principle applies to algebra. When we multiply binomials using FOIL, we get a quadratic trinomial. When we factor a quadratic trinomial, we reverse that process to find the original binomials.
This lesson explores the reverse FOIL method, which is often the first and most efficient technique for factoring quadratic expressions when the leading coefficient is 1.
Understanding Factors
A factor is a number or expression that divides another number or expression evenly. When all factors are multiplied together, the original number or expression is retrieved.
Numerical Example
Consider the number 12. To factor 12, find numbers that divide 12 without leaving a remainder: