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- Quadratic Equations – Factoring Method To Solve!
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## Quadratic Equations – Factoring Method To Solve!

**Solving quadratic equations with factors**

Quadratic equations are quadratic equations and there are many ways to solve them. Quadratic equations are similar to quadratic trinomials (most often when written in standard form); can be solved using the factor method for trinomials.

If students know how to factor a quadratic trinomial, then it is very easy for these students to solve many quadratic equations using this method.

For example; consider that there is the given equation **“x² + 6x + 8 = 0” **and we are asked to fix it. If we analyze this equation, the left side is a standard quadratic trinomial and can be easily factored.

Let’s start solving the equation as shown below:

**x² + 6x + 8 = 0**

Find two factors of “8” that add up to “6”. By brainstorming for the factors of the number ‘8’, we find that the numbers ‘4’ and ‘2’ are the necessary factors of ‘8’ which add up to ‘6’.

Therefore, we can factor the given polynomial **“x² + 6x + 8”** to, **“(x + 2) (x + 4)”** and we can rewrite our quadratic equation using the above factors as shown below:

**(x + 2) (x + 4) = 0**

Now the given factors are multiplied together to give zero (on the right side of the equation). As you know, if two numbers are multiplied to give zero, then either of them is equal to zero or both of them are equal to zero. Therefore, we can separate the two factors by writing them individually equal to zero, as shown below:

**x + 2 = 0 or x + 4 = 0**

Now, if we solve the above linear equations, we get two values of “x” as shown in the next step:

**x = – 2 or x = – 4**

Hence, the solution of the given equation has been found and can be written as shown below:

**x = -2, -4**

Students can display all work together as shown below:

**x² + 6x + 8 = 0**

**(x + 2) (x + 4) = 0**

**x + 2 = 0 or x + 4 = 0**

**x = – 2 or x = – 4**

**x = -2, -4** is the answer

Therefore, many quadratic equations can be solved using the factor method, but students should know how to factor quadratic polynomials. You can read my articles on factoring quadratic trinomials for more help.

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