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What is Factorization Formula? How to Find Factors of a Quadratic Equation?


In this article, you will learn what factorization formula is and how to do factorization.

What is Factorization?

The process of finding factors of quadratic equations to find the solution is called factorization. The factor of a number refers to a non-zero number that divides it without leaving the remainder. The factorization breaks the number to find its multiple.

In algebra, factorization is used to find two numbers whose product and sum are given in the equation. It breaks down the product of two numbers into two smaller numbers known as factors of the expression.

Factorization Formula in Algebra

In algebra, the factorization formula helps to convert an algebraic expression into simple form by using its factors. For example, if we have a quadratic equation,

ax2 + bx + c = 0

To convert it in simple form, the factoring formula break the middle value into two numbers such that,

factorization formula
factorization formula

The factorization formula is used to find factors of any number or algebraic expression easily. It is a decomposition method that breaks a number into products of other factors.

Factoring Formula

In mathematics, the factorization may refer to prime factorization, GCF or HCF. It makes the factors of a number or integers. For example, prime factorization of 12 is,






Here 1, 2, 3, 4 and 6 are factors of 12 and 1, 2 and 3 are prime factors.

How to Find Factors of a Quadratic Equation?

Basically, you can compute factors of an expression by finding two multiples of the middle coefficient. But here we are providing you an easy and step-by-step method to find factors.

1. Arrange the equation in standard form such that,

ax2 + bx + c = 0

2. Find the factors of b such that

b1 + b1 = b
b1 x b2 = ac

3. Use the factors of b in the equation by using the factoring formula.

4. Solve the equation to find the solution of x.

find factorization
find factorization

How to Use Prime Factorization to Find LCM?

You can find the LCM by using prime factorization easily. Use the following steps to find LCM.

  1. Find the prime factorization of each number.
  2. Write each number as a product of prime factors.
  3. Bring down the primes in each column.
  4. Find the least common factor.

For example, the prime factorization of 12 and 18 are,




Formula's Related to Factoring Formula

  1. Square of a sum
  2. $$ (a+b)^2=a^2+2ab+b^2 $$
  3. Square of a difference
  4. $$ (a-b)^2=a^2-2ab+b^2 $$
  5. Difference of square
  6. $$ (a^2-b^2)=(a+b)(a-b) $$
  7. Difference of cube
  8. $$(a^3-b^3)=(a-b)(a^2+ab+b^2)$$
  9. Sum of cube
  10. $$(a^3+b^3)=(a+b)(a^2-ab+b^2)$$


How to Find GCF using Prime Factorization?

GCF stands for greatest common factor that is the largest common factor by which two or more numbers can be divided. You can use the following steps to find GCF.

  • Find the prime factorization of each number.
  • Write each number as a product of prime factors.
  • Bring down the primes in each column.
  • Find the greatest common factor.
  • For example the GCF of 12 and 30 is 6.

What are the 5 Factoring Techniques?

These are:

  • Factoring out GCF
  • Sum and product pattern
  • Grouping method
  • Perfect square method
  • Difference of square method

What is Common Factoring in Math?

The common factoring is a technique of finding factors of two or more numbers. It is done by using prime factorization of all numbers, when it is done, we find the common factors from them.

Alan Walker

Last updated: July 07, 2023

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.