# Uses of Factorization

🏆Practice solution of equations using factoring

Factorization is the main key to solving more complex exercises than those you have studied up to today.
Factorization helps to solve different exercises, among them, those that have algebraic fractions.
In exercises where the sum or difference of their terms equals zero, factorization allows us to see them as a multiplication of $0$ and thus discover the terms that lead them to this result.

For exercises composed of fractions with expressions that may seem complicated, we can break them down into factors, reduce them, and thus end up with much simpler fractions.

## Test yourself on solution of equations using factoring!

Find the value of the parameter x.

$$(x-5)^2=0$$

## Let's look at some examples

If we are presented with an exercise like the ones we mentioned before, where the total equals $0$:
$x^2+5x+4=$

we can factor it in one of the ways that allow us to do so, and we will immediately have the solutions.
The factorization will be as follows:
$(x+4)(x+1)=0$
and the results will be $x=-1,-4$

Another example:
$2x^2+2x=0$

If we factor it, we will obtain:
$2x(x+1)=0$
Therefore, the solutions are: $x=0, -1$

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## Examples and exercises with solutions on the uses of factorization

### Exercise #1

Find the value of the parameter x.

$(x-4)^2+x(x-12)=16$

### Step-by-Step Solution

Let's open parentheses, remembering that there might be more than one solution for the value of X:

$(x-4)^2+x(x-12)=16$

$x^2-8x+16+x^2-12x=16$

$2x^2-20x=0$

$2x(x-10)=0$

Therefore:

$x-10=0$

$x=10$

Or:

$2x=0$

$x=0$

$x=0,x=10$

### Exercise #2

Find the value of the parameter x.

$(x-5)^2=0$

### Video Solution

$x=5$

### Exercise #3

Find the value of the parameter x.

$x^2-25=0$

### Video Solution

$x=5,x=-5$

### Exercise #4

Find the value of the parameter x.

$2x^2-7x+5=0$

### Video Solution

$x=1,x=2.5$

### Exercise #5

Find the value of the parameter x.

$-x^2-7x-12=0$

### Video Solution

$x=-3,x=-4$