


Third Example3x^{4}  288x^{2}  1200 = 0 Steps 1 and 2All three terms are already on the left side of the equation, so we may begin factoring. First, we factor out a greatest common factor of 3. 3(x^{4}  96x^{2}  400) = 0 Next, we factor a trinomial. 3(x^{2} + 4)(x^{2}  100) = 0 Finally, we factor the binomial (x^{2}  100) as a difference between two squares. 3(x^{2} + 4)(x + 10)(x  10) = 0 Step 3We proceed by setting each of the four factors equal to zero, resulting in four new equations. 1. 3 = 0 The first equation is invalid, and does not yield a solution. The second equation cannot be solved using basic methods. (x^{2} + 4 = 0 actually has two imaginary number solutions, but we will save Imaginary Numbers for another lesson!) Equation 3 has a solution of x = 10, and Equation 4 has a solution of x = 10. Step 4We now include all the solutions we found in a single solution to the original problem: x = 10, 10 This may be abbreviated as x = ??10 

