Find the value of the parameter x.$$ 12x^3-9x^2-3x=0 $$

$$ x=0,x=1,x=-\frac{1}{4} $$

$$ x=0,x=-1,x=\frac{1}{4} $$

$$ x=0,x=1,x=-\frac{1}{4} $$

$$ x=\frac{1}{4},x=1,x=-1 $$

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$$ 8,8,\frac{8}{\sqrt{2}} $$

Uses of Factorization

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.

Detailed explanation

Start practice

Test yourself on solution of equations using factoring!

Find the value of the parameter x.

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

Practice more now

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: $x=0, -1$

If you are interested in this article, you might also be interested in the following articles:

Factorization
Factorization according to short multiplication formulas
Factorization through the extraction of the common factor outside the parentheses
Factorization of trinomials
Factorization of algebraic fractions
Addition and subtraction of algebraic fractions
Simplification of algebraic fractions
Multiplication and division of algebraic fractions
Solving equations through factorization

In the blog of Tutorela you will find a variety of articles about mathematics.