Quadratic Equations - Factoring Method To Solve!

By Manjit Singh Atwal
Solving Quadratic Equations Using Factors

Quadratic equations are degree two equations and there are many ways to solve them. Quadratic equations are similar to quadratic trinomials (most often when written in the standard form); they can be solved by 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 there is the given equation "x² + 6x + 8 = 0" and we are asked to solve this. If we analyze this equation, the left side is a standard quadratic trinomial and it can be factored easily.

We start to solve the equation as given below:

x² + 6x + 8 = 0

Find two factors of "8" which add upto "6". By brain storming for factors of number "8", we find that numbers "4" and "2" are the required factors of "8" which add up to "6".

Hence, 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 multiply with each other to give zero (on right hand side of the equation). As you know, if two numbers multiply to give zero, then either of them is equal to zero or both of them equal to zero. Therefore, we can separate both the factors by writing them equal to zero individually 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 have been found and which can be written as shown below:

x = -2, - 4

The students can show the whole work all 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 by 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.