Understanding Degree 2, 3 and 4 Polynomial Inequalities

Understanding Degree 2, 3 and 4 Polynomial Inequalities Making engineering education more understandable to students can be difficult due to the demanding mathematical requirements of the major. This is especially true for mathematically underprepared students. One specific area of great difficulty for under-prepared students is graphing functions. Graphing is critical for being successful in calculus. The current method in algebra textbooks for solving polynomial inequality problems uses the Interval Method. This method sets the polynomial equal to zero and is then subsequently solved. The solution values are called Critical Numbers. These numbers are plotted on a number line and the associated intervals are formed. This can be confusing later in calculus, because critical numbers have a different meaning in that course. The student then selects a test number from each interval and plugs that number into the inequality to determine if you get a true or false statement. This is basically a set of instructions the student must follow and for most students does not relate to graphing. To help improve their graphical skills the following method will be used. First the Critical Numbers from the above method are the x-coordinates for the x-intercepts of the polynomial (x,0). The first change is to call them x-intercepts not Critical Numbers. This helps reinforce common aspects of graphs, x, and y intercepts. Students at this point have seen parabolas (Degree 2 Polynomials). The x-intercepts are plotted on the x-y plane (not just a number line) and a rough sketch of the parabola is drawn. The student can now visually find the correct interval solutions. For Degree 3 and 4 polynomials the End Behavior for both polynomials is given. This reinforces graphing which will help them in their first calculus course. At this time only fully factored degree 3 and 4 polynomials will be given. The students can read the x-intercepts from the equation. The student graphs the polynomial with the associated End Behavior and once again the solution is visually obtained. To simplify the procedure only linear factors with multiplicity one will be used. This paper is not written from a research perspective. There was no collected student data from surveys as to the effectiveness of this alternative method.