Lesson 7

Refresher

 

Review the following examples to see how to factor quadratic equations. Once you have reviewed some examples, try some questions to make sure you understand the concepts provided here.

 

Example 1

 

x2 + 5x + 4 = 0

 

Since 1 and 4 have a sum of 5 and a product of 4, x2 + 5x + 4 = 0 is the same as

 

 

Example 2

 

x2 − 9x + 20 = 0

 

Since −4 and −5 have a sum of −9 and a product of 20, x2 − 9x + 20 = 0 is the same as

 

 

Example 3

 

x2 − 4x − 32 = 0

 

Since 4 and −8 have a sum of −4 and a product of −32, x2 − 4x − 32 = 0 is the same as

 

 

Example 4

 

2x2 + 4x − 30 = 0

 

The equation has a common factor of 2.

 

2(x2 + 2x − 15) = 0

 

Since −3 and 5 have a sum of 2 and product of −15, 2(x2 + 2x − 15) = 0 is the same as

 

 

Example 5

 

y2 − 16 = 0

 

Since both terms on the left side are squares, this is a difference of squares (16 = 42).

 

 

Example 6

 

−5y2 + 125 = 0

 

The equation has a common factor of −5.

 

−5(y2 − 25) = 0

 

Since both terms inside the brackets are squares, treat this like a difference of squares.

 

 

Example 7

 

x2 − 8x + 16 = 0

 

The equation has the form of a perfect square since −8x = 2(−4x) and 16 = (−4)2.

 

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Now that you have had an opportunity to review some examples, solve the following factoring questions to ensure you understand the concepts presented here.

1. 2x2 + 8x + 8 = 0 Answer
   
   
2. 2x2 + 5x − 3 = 0 Answer
   
   
3. 4x2 + 5x − 6 = 0 Answer

Go to How to Find Zeros, Minimums, and Maximums with Your Graphing Calculator to see directions for finding the zeros of a function for a graphing calculator. You may have to adapt the directions if you are using a calculator from a different manufacturer.

 

Go back to the Are You Ready? section, and try the questions again. If you are still having difficulty, contact your teacher.