# What is a quadratic equation? How can you solve a quadratic equation by the factorization method?

An algebraic expression in the form of ax^{2 }+ bx + c = 0 is called a quadratic equation. It has a degree value of 2.

## Answer: An algebraic expression in the form of ax^{2 }+ bx + c = 0 is called a quadratic equation. We can solve a quadratic equation by the factorization method by determining the factors of the equation.

Let's understand how to determine the factors of a quadratic equation in detail.

**Explanation:**

The solution to a quadratic equation can be found using different methods such as completing the squares, quadratic formula, factorization, etc.

Following are the steps to solve an equation using the factorization method.

Step 1: Convert the quadratic equation in standard form.

Let ax^{2 }+ bx + c = 0 is standard form of the equation.

Step 2: Split the middle term that is coefficient of x as a sum or difference of factors of a × c.

⇒ Let b_{1 }and b_{2} be the sum of factors.

⇒ Product of the factors be ( a × c ) = ( b_{1 }+ b_{2 }) sum of the factors.

⇒ ax^{2 }+ (b_{1 }+ b_{2}) x + c= 0

Step 3: By taking out the common factors, we get the desired factors.

Let us solve the quadratic equation x^{2} - x - 6 = 0

⇒ x^{2} - x - 6 = 0

⇒ x^{2} - 3x + 2x - 6 = 0

⇒ x (x - 3) + 2(x - 3) = 0

⇒ (x - 3) (x + 2) = 0

You can use Cuemath's Quadratic Factoring Calculator to find the factors of the quadratic equation.

### Thus, we can solve the quadratic equation by using the factorization method.

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