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Tuesday, May 14, 2013

Special Products - Factoring, 2

Category: Algebra

"Published in Newark, California, USA"

Find the factors for


Solution:

The given equation above is a quadratic equation where the variables or terms are polynomials like (2x - 1) and (x + 3). 

To test the above equation if it is factorable or not, let's consider the following procedure: if a = 8, b = -2, and c = -3, then using the discriminant formula, we have







Since the value of discriminant is a perfect square, then the given equation is factorable. Consider the given equation above



Factor the above equation in terms of (2x - 1) and (x + 3), we have








Monday, May 13, 2013

Special Products - Rational Functions

Category: Algebra

"Published in Newark, California, USA"

 Write  the product and simplify for


 

Solution:

The given equation above is another good example of special products where a binomial multiplied by another binomial where the terms are rational functions. In this case, we have to do the distribution property of multiplication over addition as follows






The LCD (Least Common Denominator) of the three fractions is (x + y)2(a + b)2. Rewrite the three fractions in terms of their LCD and simplify, we have




Since all the terms of the numerator cannot be combined and simplified, then we can leave the final answer as is.



Sunday, May 12, 2013

Inverse Trigonometric Functions

Category: Trigonometry, Algebra

"Published in Suisun City, California, USA"

Rewrite the expression as an algebraic expression in x for 



Solution:

Consider the given equation above, we have



Let

and

so that the above equation becomes







Next, we need to get the values of trigonometric functions as a function of x. Consider again the given inverse trigonometric functions in order to get the trigonometric functions as a function of x as follows:

Let 



Draw and label a right triangle in order to get the other trigonometric functions as a function of x


Photo by Math Principles in Everyday Life







Let



Draw and label a right triangle in order to get the other trigonometric functions as a function of x


Photo by Math Principles in Everyday Life







Finally, consider again the function



Substitute the values of trigonometric functions to the above equation, we have









Rationalize the denominator in order to eliminate the radical sign








Therefore,