Solve a quadratic equation by factoring

Step by Step Examples

A quadratic equation is an equation that can be written as:

ax ² + bx + c where a ≠ 0

A quadratic equation must have a squared term as its highest power

Examples of quadratic equations

  • y = 2x² + 3x + 7
  • y = 13x² + 2
  • y = x² − 4x + 15
  • y = −x² + 5

Examples of equations that are not quadratic

  • y = 11x + 223
  • y = x3 − 4x² +5x +6
  • y = 2x3 − 7x²
  • y = −x4 + 5

The solution of a quadratic equation is the value of x when you set the equation equal to zero
i.e. When you solve the following general equation:

0 = ax² + bx + c

Given a quadratic equation:

ax ² + bx + c

One method to solve the equation for zero is to factor the equations.

General Steps to solve by factoring

  • Create a factor chart for all factor pairs of c
    • A factor pair is just two numbers that multiply and give you 'c'
  • Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b
  • Insert the pair you found in step 2 into two binomials
  • Solve each binomial for zero to get the solutions of the quadratic equation.

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Example of how to solve a quadratic equation by factoring

Quadratic Equation:

y = x² + 2x + 1

Picture of steps to solve quadratic equation by factoring

Below is a picture representing the graph of

y = x² + 2x + 1
as well as the solution we found by factoring

Picture of graph of  solved quadratic formula

Use the steps above to solve the quadratic equation by factoring

quadratic equation:

y = x² − 2x + 1

Below is a picture of the graph of the quadratic

y = x² − 2x + 1
as well as the solutions

Calculate the solutions of the quadratic equation below by factoring

quadratic equation:

y = x² + 4x + 4

Steps to solve quadratic equation by factoring

Below is a picture of the graph of the quadratic y = x² − 2x + 1 as well as the solutions

Calculate the solutions of the quadratic equation below by factoring

quadratic equation:

y = x² − 4x + 4

Steps to solve quadratic by factoring

y = x² − 4x − 4
is graphed below as well as its solution (2,0)

Calculate the solutions of the quadratic equation below by factoring

quadratic equation:

y = x² + 6x + 9

Steps to solve quadratic by factoring

xy = x² +  6x + 9
is graphed below as well as its solution (2,0)

Calculate the solutions of the quadratic equation below by factoring

quadratic:

y = x² − 6x + 9

y = x² − 6x + 9
  • c = 9
  • b = 6
  • The only factors of c whose sum is b are -3 • -3
  • y = (x − 3)(x − 3)
  • 0 =(x − 3)
  • The solution is at x = 3

Use the steps to solve the equation below

quadratic equation:

y = x² + 2x − 3

Steps to solve quadratic by factoring

y = x² + 2x − 3
is graphed below as well as both the solutions

Use the steps to solve the equation below

quadratic equation:

y = x² − 2x − 3

Steps to solve quadratic by factoring

y = x² − 2x − 3
is graphed below as well as both the solutions