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Tuesday, November 5, 2013

Special Products - Factoring, 25

Category: Algebra

"Published in Newark, California, USA"

Find the factors for


Solution:

Consider the given equation above


Did you notice that the given equation is a quadratic equation of variable x? The coefficient of three terms are also variables. In this type of quadratic equation, we have to do the trial and error method in factoring until we get the desired middle term. Since the coefficient of variables are already factored, then we can start to factor the given equation as follows



The middle term is 





Since the value of the above calculation is the same as the middle term of the given equation which is 4x, then the factors of the given equation are

 

Monday, November 4, 2013

Special Products - Factoring, 24

Category: Algebra

"Published in Suisun City, California, USA"

Find the factors for


Solution:

Consider the given equation above


Did you notice that the first three terms of the given equation is a perfect trinomial square? Well, let's group the first three terms as follows



At the last three terms, when you group and take out their negative sign, then it will be a perfect trinomial square, too as follows
 
  

Next, rewrite the grouped terms in terms of exponential function as follows
 
 
 
Since the above equation can be factored by the difference of two squares in which the grouped terms are considered as a single term, then the factors of the given equation are
 
 
 
 

Sunday, November 3, 2013

Special Products - Factoring, 23

Category: Algebra

"Published in Suisun City, California, USA"

Find the factors for


Solution:

Consider the given equation above


Did you notice that the first four terms of the given equation is a perfect cube? Well, let's group the first four terms as follows



Next, rewrite the grouped terms in terms of exponential function as follows



Since 64 is a perfect cube, then we can factor the above equation by the difference of two cubes. Therefore, the factors of the given equation are