Factoring Polynomials: Learn It or Die!
Ask any adult if they know how to factor a polynomial. Most will say “What?”. Some will say “I learned that in high school, but I couldn’t tell you how to do it now”. If you happen to be asking an engineer or a scientist, they’ll probably say “Sure! It’s fun, but not really useful”. So why do we, as math educators insist that students must not only know how to factor polynomials but must master the subject as if their very lives depended upon it?
Most math educators would agree with the engineer’s first statement. It is fun. But why is it fun? The answer is that it is a puzzle, a mental exercise that yields satisfaction when solved. But let’s examine its utility. Factoring polynomials does lead to the Fundamental Theorem of Algebra (Wow! That sounds regal). It does lead to completing the square to solve a quadratic polynomial, which, in turn, leads to the quadratic formula. Are some adults required to solve a polynomial equation? The answer is yes. engineers, scientists, actuaries, programmers, and others are sometimes required to solve polynomial equations. But rarely is the solution even rational, much less an integer. Since the solution must be approximated, the clever maneuvers learned in high school are not applicable.
So why bother to teach factoring at all? The answer is that we, as educators, have been charged with teaching our students to think, to enjoy thinking, and to trust the results of their thought. We cannot possibly teach our students everything they will need to know to be productive citizens. But we can train their minds to empower them to figure it out. Factoring polynomials should be taught once, early in the math curriculum, not as a useful life skill, but as mental exercise to hone the mind. The trend in math education is to offer students various gimmicks or procedures (the X method, slide and glide, etc.) to allow students to factor a polynomial without really thinking about it. The mind is not honed. The procedures are robotic and forgotten as soon as they are regurgitated on a test.
That being said, here is a link to a great way to factor a polynomial.