Algebra I: 1,001 Practice Problems For Dummies

Chapter 15

Solving Polynomials with Powers Three and Higher

A polynomial is a smooth curve that goes on and on forever, using input variables going from negative infinity to positive infinity. To solve a polynomial means to set the equation equal to 0 and determine which, if any, numbers create a true statement. Any numbers satisfying this equation give you important information: They tell you where the graph of the polynomial crosses or touches the x-axis.

The Problems You'll Work On

Solving polynomials in this chapter requires the following techniques:

• Counting the number of possible real roots/zeros, using Descartes's Rule of Signs
• Making a list of the possible rational roots/zeros, using the Rational Root Theorem
• Putting Descartes's Rule of Signs and the Rational Root Theorem together to find roots
• Applying the Factor Theorem
• Solving polynomial equations by factoring
• Applying synthetic division

What to Watch Out For

As you probably know, you can come up with a different answer to a math problem by simply confusing or forgetting one step; here are some things to watch out for:

• Confusing real roots with rational roots; rational roots are real, but real roots aren't necessarily rational
• Being sure to list all the possible divisors of a number, not missing multiples
• Remembering to change the sign of the numerical part of the divisor when using synthetic division
• Taking roots with multiplicity of more than one into account when looking for factors

Applying Descartes's Rule ...