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 of Signs to Count Real Roots
656–659 Count the possible number of positive and negative real roots of the equation.
656.
657.
658.
659.
Applying the Rational Root Theorem to List Roots
660–663 List all the possible rational roots for each polynomial equation.
660.
661.
662.
663.
Determining Whether Numbers Are Roots
664–667 Check to see which of the given values are roots of the equation.
664. Given
665. Given
666. Given
667. Given
Solving for the Roots of Polynomials
668–685 Solve for all real roots.
668.
669.
670.
671.
672.
673.
674.
675.
676.
677.
678.
679.
680.
681.
682.
683.
684.
685.
Chapter 16
Reining in Radical and Absolute Value Equations
Aradical equation contains at least one term that’s a square root, cube root, or some other root. When solving radical equations, you apply a method that’s effective but comes with a built-in error possibility; you may find (and need to recognize) extraneous solutions. You need to rewrite absolute value equations to solve them. The solutions of the rewrites are then the solutions of the original equation.
The Problems You’ll Work On
Here’s just a sampling of the radical things you work on in this chapter:
Rewriting equations with only two terms and squaring both sides to solve
Squaring both sides of an equation when starting with three terms
Dealing with more than one radical term
Catching extraneous solutions
Graphing absolute value statements for clarity
Solving absolute value equations after writing corresponding equations
Checking for nonsense answers
What to Watch Out For
Here are a few things that may rock your boat, so be on the lookout:
