A Step-by-Step Guide to Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring
Solving Quadratic Equations by Factoring

I believe that solving quadratic equations is an important skill that every high school student must master. While there are several methods to solve quadratic equations, factoring is perhaps the most elegant and straightforward method of all.

Not only does the factoring method allow students to understand the problem better, but it is also a versatile tool that can be applied to many other areas of math.

Read on to explore the process of solving quadratic equations by factoring its importance and some examples to help you understand it better.

If you are interested in learning how to solve quadratic equations by completing the square, I wrote a whole article detailing everything you need to know.

What Are Quadratic Equations?

Quadratic equations are second-order polynomial equations in a single variable x raised to the power of 2. For example, ax2 + bx + c = 0, where a,b, and c are constants. Since quadratic equations are second-order polynomial equations, the fundamental theorem of algebra guarantees that they have at least one solution.

There are generally four ways to solve a quadratic equation, including:

  • Factoring
  • Completing the square
  • Using the quadratic formula
  • Graphing.

What are quadratic equations used for? Quadratic equations are helpful in various real-life situations, including calculating the speed of an object, the areas of an enclosed space, maximizing or minimizing, or graphing a piece of equipment for designing.

If you want to learn more about quadratics equations, I encourage you to check out Khan Academy or watch the video below.

Solving Quadratic Equations by Factoring

Solving quadratic equations by factoring is an essential skill as it provides the basis for working with other complex mathematical concepts, such as graphing quadratic equations.

Here are the steps to solve quadratic equations by factoring:

Step 1: Rewrite The Quadratic Equation in Standard Form

The first step in solving quadratic equations by factoring is to rearrange the equation so that one side equals zero. From the equation, a quadratic factor is formed by identifying two factors that multiply together to give the constant c and add together to give the coefficient b.

The standard form of a quadratic equation is ax2 + bx + c = 0, where a, b, and c are coefficients. The first step to solve any quadratic equation by factoring is to rearrange it in standard form.

Let’s take the example equation x2 + 5x = -6. To rearrange it in standard form, we simply move the constant term to the left side of the equation: x2 + 5x + 6 = 0

Step 2: Factor The Quadratic Expression

The next step is to factor the quadratic expression on the left-hand side of the equation. Factorization is the process of finding two numbers that multiply to give you the quadratic expression.

In our example, the quadratic expression is x2 + 5x + 6. To factor this expression, we need to find two numbers whose sum is 5 and whose product is 6. The two numbers are 2 and 3. Thus, we can factor the quadratic expression as (x + 2)(x + 3).

Step 3: Apply The Zero Product Property

The zero product property states that if the product of two numbers is zero, then at least one of the numbers must be zero.

In our example, the product of (x + 2)(x + 3) is zero, which means that either x + 2 = 0 or x + 3 = 0. So, we have two possible solutions: x = -2 and x = -3.

Step 4: Check Your Answers

The last step is to check your answers by substituting them into the original equation and verify that they make the equation true.

In our example, if we substitute x = -2 and x = -3 into the equation x^2 + 5x + 6 = 0, we get: (-2)2 + 5(-2) + 6 = 0 and (-3)2 + 5(-3) + 6 = 0. Both of these equations are true, which means that our answer is correct.

Watch the video below to learn how to solve quadratic equations by factoring.

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Wrapping Up

Factoring quadratic equations is an essential skill that every math student should master because it is a powerful technique that allows students to solve many quadratic equations faster and helps them understand the nature and behavior of quadratic equations better.

By following the steps outlined in this article, you can confidently solve any quadratic equation by factoring.


I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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