Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewFactoringFactor each of the following as much as possible.1.2.2100x − 81SolutionWe have a difference of squares and remember not to make the following mistake.2100x−81 ≠( 10x−9) 2This just simply isn’t correct. To convince yourself of this go back to Problems 1 and2 in the Multiplying Polynomials section. Here is the correct answer.2100x − 81 = 10x− 9 10x+92100x + 81( )( )SolutionThis is a sum of squares and a sum of squares can’t be factored, except in rare cases,so this is as factored as it will get. As noted there are some rare cases in which a sumof squares can be factored but you will, in all likelihood never run into one of them.3.23x+ 13x−10SolutionFactoring this kind of polynomial is often called trial and error. It will factor as( ax + b)( cx + d )where ac = 3 and bd = − 10 . So, you find all factors of 3 and all factors of -10 andtry them in different combinations until you get one that works. Once you do enoughof these you’ll get to the point that you can usually get them correct on the first orsecond guess. The only way to get good at these is to just do lot’s of problems.Here’s the answer for this one.23x + 13x− 10 = 3x− 2 x+5( )( )4.225x+ 10x+1SolutionThere’s not a lot to this problem.225x + 10x+ 1= ( 5x+ 1)( 5x+ 1) = ( 5x+1) 2When you run across something that turns out to be a perfect square it’s usually bestwrite it as such.5.4x −8x − 32x5 4 3© 2006 Paul Dawkins 18http://tutorial.math.lamar.edu/terms.aspx