Expert: Richard J. Raridon - 11/11/2008

Question
My friend Lauren and I are creating an educational powerpoint presentation on the seven types of factoring for our College Algebra teacher. Our seven types are Common factors [x(x+3)=x^2+3x], Trinomials [x^2+3x+4], Sum and Difference of Cubes [27x^3-1], Special Square Trinomials [9x^2+16x+25], Grouping [x^3-3x^2
+4x+2], Difference of Squares[4x^2-25], Square Trinomials[x^2-6x+9]. We would like to know the resons for using the different types of factoring, as in how it's used in the real world. Your help is greatly appreciated!
Thanks,
Genna(15) and Lauren (17)

Answer
Out in the real world factoring doesn't come up very often.  You pick the type of factoring depending upon the expression you want to factor.  For example, if you have 4x^2-25 you can simply look at it and see that the factors are (2x-5) and (2x+5).  Or you can look at
9x^2+16x+25 and see that it is (3x+5)^2.  In other words, people don't generally think about looking down a list of factoring types. They just look at an expression and see how to factor it.