What is factoring?

What is factoring in algebra? Factoring is the process by which one tries to make a mathematical expression look like a multiplication problem by looking for factors. Basically, factoring reverses the multiplication process.

• Factoring can be as easy as looking for 2 numbers to multiply to get another number. For example, It is not hard to see that 32 = 4 × 8 once you know your multiplication table.

• When factoring, you could also be looking for the prime factorization of a number. For example 81 = 3 × 3 × 3 × 3. 

• Or you may try to factor out the greatest common factor. For example, 2x + 10 = 2(x + 5) and 2 is the greatest common factor.

• Finally, you may try to factor expressions as complicated as x² - 14x - 32, 15x² - 26x + 11, or 150x³ + 350x² + 180x + 420.
  
  

Both numerical and algebraic expressions can be factored using some specific method(s). A list of the different types of factoring are given in this lesson. Check them out so you can learn the specific method of factoring.

The simplest expressions to factor are of course numerical expressions. However, looking for the prime factorization of a big number like 240 may require a lot more work. 

The lesson below about factoring integers will show you how to factor 240 and other big numbers. Then, you will be ready to factor algebraic expressions such as x² + 5x + 6 and more complicated expressions using a variety of methods.

There are three concepts you will need to understand very well before you attempt to factor an expression. Start by studying the topics in the introduction.

What is factoring in algebra? Here are the different types of factoring

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