In this algebra lesson, we will discuss how factoring can be used to solve Quadratic Equations, which are equations of the form:
ax2 + bx + c = 0 where a, b and c are numbers and a ≠ 0.
The simplest way to factoring quadratic equations would be to find common factors. Sometimes, the first step is to factor out the greatest common factor before applying other factoring techniques.
In some cases, recognizing some common patterns in the equation will help you to factorize the quadratic equation. For example, the quadratic equation could be a Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.
In other cases, you will have to try out different possibilities to get the
right factors for quadratic equations. This is still manageable if the
coefficient of x2 is 1. If the
coefficient of x2 is greater than 1 then you may want to consider using the Quadratic formula.
We can factorize quadratic equations by looking for values that are common.
|Example:||x2 + 3x = 0|
|We find that the two terms have x in common. We “take out” x from each term.|
|x(x + 3) = 0|
|We have two factors when multiplied together gets 0. We know that any number multiplied by 0 gets 0. So, either one or both of the terms are 0 i.e.|
x = 0 or
This tells us that the quadratic equation x2 + 3x = 0 can have two values (two solutions) for x which are x = 0 or x = –3
Factoring Quadratic Equations using Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.
Factoring Quadratic Equations where the coefficient of x2 is 1.
Factoring Quadratic Equations where the coefficient of x2 is greater than 1
Factoring Quadratic Equations by Completing the Square
Factoring Quadratic Equations using the Quadratic Formula.