What is factoring in math

Factoring and Factoring

You can learn how factoring works here. Let's look at this:

  • A Explanation how to factor or factor.
  • Examples how to factor out simple numbers, variables and powers.
  • Tasks / exercises so that you can practice this yourself.
  • A Video to factoring out or factoring.
  • A Question and answer area to this topic.

Tip: The factoring out is the inverse of multiplying. You can learn how this works by multiplying it in brackets.

Explanation in brackets

Let us first briefly clarify what is meant by factoring or factoring.


Definition: Factoring / Factoring

Factoring or factoring is used to make a product out of a sum or a difference.

In the simplest case, you can see directly with every term of a sum or difference that the same numbers or variables are present and can put them in front of a bracket.

Example 1: Factoring the sum / difference

Let's look at two simple equations. The first is a sum (+) and the second is a difference (-). First take a quick look at the two equations for yourself. These are explained below.

For both 3x and 3y we have a 3. For this reason we can exclude this. X + y remains in the brackets. In the second example we have 8a and - 8b. In both cases there is an 8. For this reason we can exclude 8. A - b remains in the brackets. If we were to multiply the right side of the equations out again, we would get the left side of the equations again.

Example 2: Exclude variables

Not only numbers can be excluded, but also variables. The next two equations show how this works. In the first equation, there is an x ​​in both terms. Therefore we prefer this to the bracket with y + z in it. If we multiply the right hand side, we get xy + xz again. The same game in the second equation, only with a.

So much for a few simple examples. Now is the time for more challenging tasks.


Examples in brackets

In this section, we'll look at examples of polynomial factoring and prime factorization.

Example 3: Factoring a polynomial

In this example a polynomial is to be factored. In the first step we write out all potencies. Then we look for the common variables from the three terms. So both x and y appear twice. These are marked in color for a better overview. We put everything that occurs in each term in front of the brackets. The first term is left with xx. The second term only leaves x. We find the third term completely in front of the bracket. For this reason we also write a 1 in brackets. Reason: When multiplying, y must again2x2 come out. And this is obtained by multiplying by 1.

Example 4: prime factorization

Sometimes it is also necessary to perform a prime factorization first. That sounds very complicated now, but it is actually very simple. We go here first and turn a number into a multiplication of the smallest possible numbers. We can also exclude these: The 2 · 2 occurs in both terms and can therefore be placed in front of the brackets. What remains is the front x2 and 12z2. When it comes to variables, there is no common ground between the terms, so we cannot exclude anything here.


Factoring out / factoring in binomial formulas:

The binomial formulas also make it possible to generate brackets - i.e. to factor them out or factorize them - or, conversely, to multiply them out. You can learn how this works under binomial formulas.

Exclude tasks


Factorize video

Examples and explanations

Factoring or factoring is about factoring out common numbers or variables. It is very important that you learn how to use brackets. This is exactly what the next video starts with. Then examples are calculated with explanations of how to exclude.

Next video »

Questions with answers to factoring out

In this section we look at typical questions with answers to factoring out.

Q: Is it possible to expand fractions?

A: Sometimes this works (also makes sense). Fractions are nothing more than numbers. For this reason, they can also be excluded if they occur in the respective terms. Alternatively, you can do this by expanding or shortening fractions.

Q: What topics should I look at next?

A: For example, when it comes to equations, these topics would be suitable: