In math, factoring involves finding the two or more numbers or expressions that multiply together to create another expression. This can be done with polynomials, which have two or more parts to the equation, or trinomials, which have three parts to the equation.

Basic Factoring of Numbers

At the very beginning, it’s possible to factor whole numbers. For instance, the number 15 has factors of 3 and 5. These two numbers are the numbers that can be multiplied together to get the number 15. Practicing with this can help a student understand and remember how factoring works before they start doing more complex problems.

Factoring Polynomials – Basic Examples

When expressions are used instead of whole numbers, factoring can be more difficult. Factoring polynomials includes finding two or more expressions that can be multiplied together to create a third one. A basic example of this is 12x+4, with 12x and 4 being the two parts of the equation. The number 4 is common to both parts of the expression, so it can be pulled out, leaving 3x+1. The answer, then, is 4(3x+1). It’s necessary to pull out the largest common factor to solve these equations.

Factoring Trinomials

Trinomials are made of 3 parts and are typically formatted like x^2+ax+bx. Instead of pulling out one number like the previous example, two expressions can be found that will multiply to get the original equation. For example, the equation is x^2+4x+3. One way to solve this is to find out which numbers multiply to get the number in the “b” position and add together to get the number in the “a” position. For this example, 3 and 1 are the only two numbers that can multiply to be 3 and add to be 4. The x^2 is also taken apart, since x multiplies by itself to get x^2. So, the answer for this is x^2+4x+3=(x+1)(x+3). The numbers are placed inside the parenthesis to show they are multiplied together to get the answer. When multiplied together again, the (x+1) and (x+3) combine to create the original equation.

Factoring Polynomials – More Advanced Problems

Math problems like these can be far more advanced. Although the previous examples have been fairly basic, polynomials can have multiple parts to them. One example of an equation involving more than three parts is x^3-3x^2y+3xy^2-y^3. This one has 4 parts to it and can be more complicated to solve than the ones with 2 or 3 parts. Once a student has done the factoring, it’s important to ensure they have the right answer. This is easy to do with factoring, as they can simply multiply the expressions together again to determine if the get the first equation. If they do, they’ve done the problems correctly. Factoring can vary from basic to far more difficult, but once a student learns how to factor equations they’ll find they can do just about any equation, including the more advanced example above. There are a few methods to learn that will make factoring much easier to do. Practice makes perfect here as it helps the student learn what method to use and how to use it to get the right answer.

MathBlog Factoring Tools

  • Use our factoring calculator to automatically calculate the factors of a number, with detailed how-to and examples. Or directly check out these examples below and learn how you can find the factors of a number yourself, fast and easy.