Solving Quadratic Equations by Factoring

Standard Form of a Quadratic Equation

Given real numbers a, b, and c, and a ≠ 0, the standard form of a quadratic equation is ax2 + bx + c = 0. Take a look at the examples below.

  • x2 − 9x + 14 = 6 is a quadratic equation that is not in standard form.
  • 3x2 − 7x + 2 = 0 us a quadratic equation that is in standard form, a = 3, b = −7, and c = 2.

A quadratic equation must be in standard form in order to use factoring to determine its solutions.

 

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring InteractivityPrepare to apply your factoring skills as you work to determine the solutions to quadratic equations. Your knowledge of the Zero Product Property also plays an important role. Click the player button to begin.

View a printable version of this interactivity.

 

 

Using Algebra Tiles to Solve Quadratic Equations

Algebra Tiles can be used to model and solve quadratic equations. Take a look at the following example. The model below represents the variable expression of an equation that is set equal to 0. What is the solution set?

Algebra Tiles

The factors represented in the model are (x + 1) and (x + 2). To determine the solutions, set each factor equal to 0 and solve for x.

Factoring x plus one

Factoring x plus 2

The solution set is {−2, −1}.

 

Solving Quadratic Equations by Factoring Review

Solving Quadratic Equations by Factoring Reviewself-check iconNow that you have explored solving quadratic equations by factoring, it is time to review your knowledge and practice what you have learned. Click the player button to get started.

 

 

 

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