How to Find the Real Zeros of a Polynomial Function

Algebra involves a lot of graphing of lines and equations. The zeros of a polynomial, sometimes called polynomial roots, are very important when it comes to graphing. Unfortunately, when we come to polynomials of degrees three and higher, we don't have clear, easy and straight-forward methods for finding those zeros. Here are steps that can do the job.

Instructions

Difficulty: Moderately Challenging

1. Study the degree of the polynomial to determine the number of zeros in the solution of the problem. Know that the polynomial function can't have more zeros than its degree.
2. Apply Descartes' Rule of Signs to determine the number of positive and the number of negative zeros.
3. Use the Rational Zeros Theorem if the polynomial has coefficients before the variable "x." Find any rational numbers that can possibly be zero.
4. Employ the techniques of long division, synthetic division and substitution to test possible rational zeros. Repeat steps three and four each time a zero (a factor) is found.
5. Remember to first try the simpler factoring methods you already know like special formulas such as difference of two squares, perfect squares as well as grouping to find zeros.