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.
What is factoring?
  • 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.

Prerequisites

Factoring integers
Important to understand in order to grasp the meaning of factor.

Finding the greatest common factor
Important to understand before factoring polynomials or expressions with at least two terms.

Multiplying binomials
Important to understand before factoring trinomials

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

Factoring algebraic expressions
Learn how to factor a polynomial or an algebraic expression with two or more terms.

Factoring trinomials
Learn to factor a trinomial that has the form x2 + bx + c

Factoring by grouping
Learn how to factor a trinomial of the form ax2 + bx + c by grouping terms.

How to factor a trinomial by getting rid of the impostor.
Learn how to factor a trinomial of the form ax2 + bx + c by getting rid of the impostor.

Factor using the box method
Probably the most straightforward way to factor a trinomial.

Factoring perfect square trinomials
Learn to factor perfect square trinomials.

Factoring using the quadratic formula
Learn to factor using the quadratic formula x2 + bx + c.

Factoring radicals
Learn how to factor and simplify radicals.


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