# How to Solve Quadratic Equations Using the Factorization Method

Step-by-Step method to solve a quadratic equation along with an example.

MATH TOPICS

### What is Factorization?

Factorization involves expressing a polynomial as a product of its factors. Factorization helps break down the equation into simpler binomial factors, which can then be solved to find the values of x. This method is particularly useful for equations that can be easily decomposed into two binomials.

### Step-by-Step Guide to Solving Quadratic Equations by Factorization:

**Step 1: Write the Quadratic Equation in Standard Form**

A quadratic equation is typically given in the standard form: ax^2+bx+c=0

**Step 2: Factorize the Quadratic Expression**

The goal is to express the quadratic expression as a product of two binomials. You need to find two numbers, p and q, such that:

The product of p and q is equal to the product of a and c.

The sum of p and q is equal to the coefficient of the linear term b.

**Step 3: Write the Factored Form**

Once you find p and q, you can write the quadratic equation as: (x−p)(x−q)=0.

**Step 4: Solve for x**

Set each factor equal to zero and solve for x:

**Either x−p=0 or x−q=0 **

**Therefore, x = p or x=q**

### Example

Let's solve the quadratic equation x^2−5x+6=0 using the factorization method.

**Write the quadratic equation in standard form:**x^2−5x+6=0.

**Factorize the quadratic expression:**In this case, a=1, b=-5 and c=6. We need to find two numbers whose product is 6 (the product of ac) and whose sum is -5 (the coefficient of b).The numbers -2 and -3 satisfy these conditions:

**(−2)×(−3)=6**and (**−2)+(−3)=−5**

**Write the factored form:**(x−2)(x−3)=0**Solve for x:**x−2=0 or x−3=0**Final Solution: Either x=2 or x=3**