What is the relationship between multiplying and factoring

The fundamental idea of multiplying is repeated addition. For example:



By taking the number five and add it itself three times we have:



In contrast, let's take the number three and add it itself five times, so: 

.

Both 3 and 5 are called factors that are numbers. We can multiply them to get another number. Multiplying can also be expressed like this:



So you have the factors:

 

You can even write any multiplication as the product of factors. On the other hands, factoring shows that you can write any nth-degree polynomial as the product of linear factors, so:



To conclude the relationship between both concepts is the product of factors.