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In elementary school you learned about the relationship between division and multiplication. For every division statement, there is a corresponding multiplication statement. Here are some examples:

 

Division Statement	Corresponding Multiplication Statement
6 ÷ 3 = 2	6 = 3 × 2
13 ÷ 5 = 2, remainder 3	13 = 5 × 2 + 3
16 ÷ 5 = 3, remainder 1	16 = 5 × 3 + 1

 

The concepts and processes for factoring polynomials are very similar to the concepts and processes for factoring numbers. So, you will first reacquaint yourself with factoring numbers.

 

Although the ideas of factors may seem simple, there are some fundamental concepts that require exploration. Try This 1 and Share 1 will explore these concepts in more detail.

 

Try This 1

1. What are the factors of 21?
2. How do you know 5 is not a factor of 21?

Save your responses in your course folder.

 

Share 1

 

With a partner or in a group, discuss the following question based on your responses to Try This 1:

 

What pattern do you see in the remainder when numbers are divided by factors versus non-factors?

 

If required, save a record of this discussion in your course folder.