# Factoring Using the Quadratic Formula

Quadratic formula is a useful tool that allows us to factor quadratic equations into the form

(x – a)(x – b). By **factoring quadratics**, we can find the solutions or roots of the equation.

In this article, we will discuss factoring using the quadratic formula.

**What is the Quadratic Formula?**

The quadratic formula states that for a quadratic equation in the form

**ax ^{2} + bx + c = 0 **

the solutions are given by:

**x = (-b ± √(b2 – 4ac)) / 2a**

Where a, b, and c are the coefficients of the quadratic equation.

To use the formula, we first identify the values of a, b, and c from the given quadratic equation.

**Example of Factoring with the Quadratic Formula**

Solve the equation x^{2} + 5x + 6 = 0 using the quadratic formula.

First, identify the coefficients ‘a,’ ‘b,’ and ‘c’ from your quadratic equation,

**a = 1, b = 5, c = 6**

Plugging into the formula:

**x = (-5 ± √(25 – 4(1)(6))) / 2(1)**

Simplifying:

x = (-5 ± √(25 – 24)) / 2

x = (-5 ± 1) / 2

Find the Roots:

x_{1} = (-5 + 1)/2 = -4/2 = – 2

x_{2} = -5-1/2 = -6/2 = -3

So, the roots of the quadratic equation are -2 and -3.

**FAQs**

### What are the steps for factoring with the quadratic formula?

Identify a, b, and c from the quadratic equation ax2 + bx + c = 0

Plug a, b, and c into the formula: x = (-b ± √(b2 – 4ac)) / 2a

Simplify the formula with the given values

The resulting factors will be in the form (x – a)(x – b)

### When should you use the quadratic formula?

Use the quadratic formula when you need to factor a quadratic equation that cannot easily be factored otherwise. It provides a straightforward way to find the linear factors.

### What are some examples of when factoring quadratics is useful?

Finding the zeros, x-intercepts, or solutions of a quadratic

Rewriting a quadratic into vertex form

Graphing parabolas and analyzing their key features

Solving quadratic inequalities and systems

Simplifying rational expressions

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