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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.
    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

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