The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.20: Solving Quadratic Equations

by Factoring

Factoring is one way to solve a quadratic equation. To use this method, students must factor the

equation and use the zero-product property. Many students forget to set the equation equal to

zero and consequently find an incorrect solution to the equation.

1. Review factoring polynomials with your students by providing these prompts:
   
   
   • Is there a greatest monomial factor?
   
   
   • Is the polynomial the difference of squares?
   
   
   • Is the polynomial factorable?
   
   
   
   


2. Review the information and example on the worksheet with your students. Be sure to explain
   the zero-product property and show students how to apply this property to find the solutions
   of the equation. Emphasize that each factor must be written as an equation that is equal to
   zero. Students can then solve for the variable. If necessary, discuss in detail the steps for
   solving the example equation by factoring.

EXTRA HELP:

Have students each write an equation that states that each factor is equal to zero. This will help

them solve the equations accurately.

ANSWER KEY:

(1)x=−4andx=− 2 (2)x=3andx= 1 (3)x=−5andx= 5 (4)x=4andx= 6

(5)x=− 1

1

2

andx=− 1 (6)x=1andx= 1

1

3

(7)x=−7andx=− 2 (8)x=−2andx= 3

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(Challenge)Kim needs to subtract 56 and 7xfrom both sides of the equation. This will create

the new equation ofx^2 +x− 56 =0. She can then factor the equation and solve forx.The

solutions arex=7andx=−8.

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214 THE ALGEBRA TEACHER’S GUIDE