To solve equations through factorization, we must transpose all the elements to one side of the equation and leave on the other side.
Why? Because after factoring, we will have as the product.
To solve equations through factorization, we must transpose all the elements to one side of the equation and leave on the other side.
Why? Because after factoring, we will have as the product.
The product of two numbers equals when, at least, one of them is .
If
then
either:
or:
or both are equal to .
Find the value of the parameter x.
\( 2x^2-7x+5=0 \)
Example to solve equations through factorization
First, we will transpose all the terms to one side of the equation. On the other side, we will leave .
We will obtain:
We see that it is a trinomial. Let's arrange the equation to clearly see the trinomial:
Now, let's factorize and we will obtain:
We can easily realize that the equation equals zero when
Therefore, the solution to the exercise is .
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Find the value of the parameter x.
We will factor using trinomials, remembering that there is more than one solution for the value of X:
We will factor -7X into two numbers whose product is 10:
We will factor out a common factor:
Therefore:
Or:
Find the value of the parameter x.
We will factor using the shortened multiplication formulas:
Let's remember that there might be more than one solution for the value of x.
According to the first formula:
We'll take the square root:
We'll take the square root:
We'll use the first shortened multiplication formula:
Therefore:
Or:
Find the value of the parameter x.
First, we'll factor using trinomials and remember that there might be more than one solution for the value of x:
We'll divide by minus 1:
Therefore:
Or:
Find the value of the parameter x.
We will factor using the shortened multiplication formulas:
Let's remember that there might be more than one solution for the value of x.
According to one solution, we'll take the square root:
According to the second solution, we'll use the shortened multiplication formula:
We'll use the trinomial:
or
Therefore, according to all calculations,
Find the value of the parameter x.
Let's open the parentheses, remembering that there might be more than one solution for the value of X:
Therefore:
Or:
Find the value of the parameter x.
\( x^2-25=0 \)
Find the value of the parameter x.
\( -x^2-7x-12=0 \)
Find the value of the parameter x.
\( (x-5)^2=0 \)