Factoring Calculator

Use our tool to factorize all your complex mathematical expressions.

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Moreover, our factoring calculator eliminates any scope for human error and provides a precise and accurate solution to your equation.
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In addition, our factoring calculator is completely free to use. Therefore, just input your equation, and it will solve it for you.

What Is Factoring?

Factoring in maths refers to simplifying a polynomial equation to expand and break it into a simple form that can perform other functions to identify the variables’ value.
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How Our Factoring Calculator Works

  • If you are struggling in an online class with a mathematical problem related to factoring, use our free factoring calculator.

  • In addition, write down the equation you want to factorize. For instance, 4x+7=2x+1 and get the correct result.

  • Moreover, once you have put the equation into factor, sit back and relax. Therefore, our factoring calculator scans the query and gives you accurate results. In addition, just click on the ‘Solve’ button, and you will get the answer.

Some Factoring Examples And Solutions

Problem 1:



(x-2) (x-3)

Problem 2:

(x-2)² – 9


(x+1) (x-5)

Problem 3:

2x² – 18


2(x+3) (x-3)

Moreover, to solve advanced equations, you can contact our experts. However, we can help you solve the complex equations. Want to calculate your GPA, you can use our free calculator. 

Factoring Polynomials

The process of obtaining the factors of a given value or an algebraic expression is called factorization. However, factoring a polynomial involves turning the polynomial into the sum of factors. Moreover, it can be shown as the sum of two or more simpler polynomials. In addition, it helps you make your polynomial simpler.

Classification of Polynomial

Depending on the terms of the polynomial, they are divided into the following categories:

Monomial: The polynomials that consist of only one term.

Example: 4x, 3y, x2,y3,3a4 etc.

Binomial: The polynomials that consist of two terms.

Example: x+1, x2– 1, y3+ 4, a+3, x2+ x, etc.

Trinomial: The polynomials that consist of three terms.

Example: x2+ x+1, x2+ y2+2, y-3x+2, etc.

Furthermore, you can also use our free page calculator.

Factoring Polynomial Techniques

Below are the steps to factorize a polynomial:

  • Check if the polynomials’s terms  have a common factor

  • Choose the best technique for factoring polynomials

  • Determine polynomial factors  by regrouping  or using algebraic identities

  • Polynomial  should be written as the product of its factors

Different Factoring Polynomials

There are different factoring polynomials formulas as follows:

  1. Greatest Common Factor (GCF)

  2. Substitution Method

  3. Grouping Method

  4. The difference in two squares method

Greatest Common Factor

Also called the Highest Common Factor (HCF). In addition, let’s determine the given polynomial’s greatest common factor to factorize it. However, it is simply a reverse procedure of the distributive law.

In the case of distributive law, we get:

p(q+r) = pq + pr

Whereas in the case of factorization, we invert the process

pq + pr = p(q+r)

Here p is the greatest common factor.

Grouping Method

Moreover, it is also known as factoring by pair. Therefore, the polynomial is distributed in pairs or grouped in pairs to find the zeros. Furthermore, the basic idea is to pair like terms together. However, we can conveniently apply the distributive property to factorize it nicely.

Example: Factorize x2– 15x+50

Firstly, find the two numbers that, on being added, give -15 as their sum, and on multiplication, give 50 as their product. The two numbers are -5 and -10, respectively, as,

(-5) + (-10) = -15

(-5) x (-10) = 50

Therefore, we can rewrite the given polynomial as;



Taking x – 5 as a common factor, we get;


However, the factors are (x – 5) and (x – 10).

Substitution Method

If the polynomial given is too complex, we can try substituting the complicated terms with simpler terms to solve the problem. However, this will make it much easier to factor out.

Example: Factorize (x – y)(x – y – 1) – 20

Let S = x-y. Now substitute S for x-y in the given expression.

(x – y)(x – y – 1) – 20 = (S)(S – 1) – 20

S2– S-20

(S – 5)(S + 4)


Difference of Two Squares Identity

In addition, this technique applies to factorize the binomial expressions in the form of 

x2– y2= (x – y)(x + y)

Example: Factorize (x+1)2– 9(x-2)2


(x+1)2– 9(x-2)2= (x+1)2– (3(x-2))2

=((x+1-3(x-2)) ((x+1)+3(x-2))


= (-2x+7)(4x-5)

Frequently Asked Questions

How can I find prime factorization?

You need to divide the number by prime factors until you get the remainder equal to 1. For instance, by prime factorizing the number 30, you will get 30/2 = 15, 15/3 = 5, and 5/5 = 1. In addition, once you receive the remainder, it cannot be further factorized.

How to do a quadratic formula?

Recognize a, b, and c in the quadratic equation a x 2 + b x + c = 0. 

Then, substitute the values from step 1 into the quadratic formula. 

Simplify, making sure to follow the order.

What is the way to multiply two binomials?

For multiplying binomials, use the FOIL method. Therefore, the full form of FOIL is First, Outer, Inner, and Last. However, FOIL is the sequence in which the terms are multiplied in this order.

How do you factor out the common factor of each polynomial?

To factor the GCF out of a polynomial, follow the steps:

  • Find the GCF of all terms in the polynomial.

  • Express the term as a product of the GCF and another factor.

  • Use distributive property to factor out the GCF.