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## Quadratic Equations – Factoring Method To Solve!

**Solving Quadratic Equations Using Factors**

Quadratic equations are quadratic equations and there are many ways to solve them. Quadratic equations are similar to quadratic trinomials (often written in the usual form); can be solved using the method of factoring trinomials.

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

For example; Consider the given equation **“x² + 6x + 8 = 0” **and we are asked to resolve this matter. If we analyze this equation, the left side is a regular quadratic trinomial and can be easily done.

We first solve the equation as given below:

**x² + 6x + 8 = 0**

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

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

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

Now the given factors multiply each other to give zero (on the right side of the equation). As you know, if two numbers are multiplied to give zero, then either one of them is equal to zero or both of them are equal to zero. Therefore, we can separate these two cases by writing them equal to zero each 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 is found and can be written as shown below:

**x = -2, -4**

Students can show all the 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 most quadratic equations can be solved using the factor method but students need to know how to estimate quadratic polynomials. You can read my article about quadratic trinomials for more help.

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