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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
  • Step 1) Create a factor chart for all factor pairs of c
    • A factor pair is just two numbers that multiply and give you 'c'
  • Step 2) Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b
  • Step 3) Insert the pair you found in step 2 into two binomals
  • Step 4) S olve 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
Solutions
Calculate the solutions of the quadratic equation below by factoring
quadratic equation: y = x² + 4x + 4
Solutions
Calculate the solutions of the quadratic equation below by factoring
quadratic equation: y = x² − 4x + 4
Solutions
Calculate the solutions of the quadratic equation below by factoring
quadratic equation: y = x² + 6x + 9
Solutions
Calculate the solutions of the quadratic equation below by factoring
quadratic: y = x² − 6x + 9
Answer
Use the steps to solve the equation below
quadratic equation: y = x² + 2x − 3
Solutions
Use the steps to solve the equation below
quadratic equation: y = x² − 2x − 3
Solutions