Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

This lesson will review the process of factoring as a method of solving quadratic equations.

Def ⁿ: Quadratic equations are normally expressed as ,
where a does not equal zero.

Tidbit of info:

“Doesn’t QUAD
mean four???”

Although in Latin the prefix "quadri" means four, the word "quadrus" means a square (because it has four sides) and "quadratus" means "squared." Consider other words such as: "quadrille," meaning a square dance; "quadrature," meaning constructing a square of a certain area.

Quadratic equations were originally used in connection with geometric problems involving squares. Since the second power is called a "square," equations with the highest power being two are called quadratic equations.

Many of the simpler quadratic equations with rational roots can be solved by factoring.

To solve a quadratic equation by factoring:

1.	Start with the equation in the form Be sure it is set equal to zero!
2.	Factor the left hand side (assuming zero is on the right)
3.	Set each factor equal to zero
4.	Solve to determine the roots (the values of x)

Let's examine some possible situations:

Factoring with GCF (greatest common factor)	Factoring with DOTS (difference of two squares)	Factoring Trinomials
Find the largest value that can be factored from each of the elements of the expression. Notice how the answers (the roots) can also be observed as the locations where the graph crosses the x-axis.	Look carefully at this example to refresh this process:	In a quadratic equation in descending order with a leading coefficient of one, look for the product of the roots to be the constant tern and the sum of the roots to be the coefficient of the middle term. Notice how the answers (the roots) can also be observed as the locations where the graph crosses the x-axis.
	Or Isolate the Variable (Square Root Property)