If all methods to solve quadratic equations are included in your syllabus, then these words “solve quadratic equations by factoring method” are not new to you. But it’s not necessary that every student is efficient in solving factorization. So, if you are also escaping from factorization and you are **finding the ****factoring quadratics calculator** then this explanation is for you. Before starting the explanation of the factoring method to solve quadratic equations we know about the factorization.

## FACTORIZATION

In mathematics any number which is exactly divisible by the other number then the other number will be the factor of that number. For instance, 12 is exactly divisible by 1, 2, 3, 4, 6, & 12 then all these numbers are the factors of 12. So, any expression which is expressed in a form of product of two or more factors is known as factorization.

## QUADRATIC EQUATION

The second-degree polynomial equation with its standard form as ax^{2} + bx + c = 0 is known as Quadratic equation and the **formula for Quadratic equation** is as:

(x = \dfrac{ -b \pm \sqrt{b^2 – 4ac}}{ 2a })

To solve quadratic equations is easy and by using the online **Quadratic formula calculator** this task becomes very easy with great accuracy of the result. But when the quadratic equations are solved by the factoring method then it is necessary to get know how about the process of factoring to become the best **Quadratic equation** **solver**. Let’s understand the process of factoring to solve quadratic equations.

## FACTORING PROCESS TO SOLVE QUADRATIC EQUATIONS

In the process of the factoring of the form of ax^{2} + bx + c = 0, we consider that the factors a and b of c (which is a third term) are found such that their sum (a + b) is equal to b (which is the coefficient of the middle term). For finding the factors of ax^{2} + bx + c = 0, we follow the following steps:

- To find “a” the coefficient of x
^{2}, “b” the coefficient of x and “c” the constant term. - To find two numbers b & c such that b + c = b and bc = ac.
- The factors of ax
^{2}+ bx + c will be (ax + b) and (x + c).

### EXAMPLE #1:

Solve the equation 2a^{2} + a – 1 by factoring method.

### SOLUTION**:**

Here a = 2, b = 1 & c = -1.

First, we multiply a with c = 2 × -1 = -2, now find the factors of -2 which are 1 & 2 and when we take it as 2 – 1 = 1 and 1 = a so, we may write it as 2a – a = a which is equal to b.

2a^{2} + 2a – a – 1

2a (a + 1) – 1(a + 1)

(2a -1) (a +1).

### EXAMPLE #2:

Solve the equation 6a^{2} + 11a – 10.

### SOLUTION:

Here a = 6, b = 11, and c = -10

By the multiplication of a and c we get 6×-10 = -60, now find the factors of -60.

1× -60, 2 × -30, 3 × -20, 5 × -12, 6 × -10, 10 × -6, 12 × -5, 15 × -4 & 60 × -1.

From the above factors of -60 if we take

15 – 4 = 11 and when we multiply these numbers, we will get the product of a × c = 60. So, 15a – 4a = 11a.

6a^{2} + 15a – 4a – 10.

3a (2a + 5) – 2(2a + 5).

(3a – 2) (2a + 5).

From the above discussion it will be clear to you how you will solve quadratic equations by factoring method. But if you have less time to submit your assignment and you need to **find the quadratic function** **calculator** then try our **factoring quadratics calculator** to solve quadratic equations in minutes with accurate results.