2.02  Quadratic Equations by Factoring

College Algebra: One Step at a Time.  Page 143 - 154   #21, 49, Extra Problem

NEW PROBLEMS:  #21, 49, Extra

Dr. Robert J. Rapalje

Seminole Community College

Sanford, FL  32773

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21.           

Notice that this is really just a TRINOMIAL, and as such, it can be factored into the product of two binomials.  In this case, the FIRST times FIRST gives you  which is . 

Next, the LAST times LAST must give you , so try  or  , where the numbers are the SAME sign.  In order for the numbers to add and give you a  you will need to put the  in the first binomial and the  in the second binomial.   Then the OUTER times OUTER will be , and the INNER times INNER will be for a total of .

 It looks like this:

Now, set each factor equal to zero, and solve for x.  There are two solutions:

49.          

Solution:  The first step in solving this equation is to square the binomial—i.e., remove the parentheses:  

The next step is to set the equation equal to zero, by subtracting from each side:

Notice that this is a trinomial which factors:

Therefore,

No Extra Charge:          

Solution:  The first step in solving this equation is to square the binomial—i.e., remove the parentheses:  

The next step is to set the equation equal to zero, by subtracting and adding from each side:

Notice that this is a trinomial which factors:

Therefore,  

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