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Quadratic Equations – Factoring Method To Solve!
Solving Quadratic Equations Using Factors
Quadratic equations are second degree equations and there are many ways to solve them. Quadratic equations are similar to quadratic trinomials (most often when written in standard form); they can be solved using the factor method for trinomials.
If students know how to factor a quadratic trinomial, then it is very easy for them 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 solve it. If we analyze this equation, the left side is a standard quadratic trinomial and it can be factored easily.
We start solving the equation as shown below:
x² + 6x + 8 = 0
Find two factors of “8” that add up to “6”. Brainstorming for the factors of the number “8”, we find that the numbers “4” and “2” are the required factors of “8” which add up to give “6”.
We can therefore 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 the right side of the equation). As you know, if two numbers multiply to zero, then one of them equals zero or both equal zero. Therefore, we can separate the two factors by writing them equal to zero individually, as shown below:
x + 2 = 0 Or x + 4 = 0
Now, if we solve the linear equations above, we get two values of “x”, as shown in the next step:
x = – 2 Or x = – 4
Hence the solution of the given equation which was found and which can be written as shown below:
x = -2, -4
Students can show the entire 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 factorial 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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