Algebra II

Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.

Polynomials and Their PropertiesFactoring and Solving Polynomial EquationsRational Expressions and Equations
Complex Numbers and Their OperationsPolynomial Division and the Remainder TheoremPolynomial and Rational Inequalities
Modeling Real-World Data with PolynomialsApplications of Rational Expressions in Science and EngineeringComplex Numbers in Electrical Engineering and Art
Mastering Word ProblemsChecking Your SolutionsSmart Use of Calculators and Technology
Polynomials and Thei...Factoring and Solvin...Rational Expressions...Complex Numbers and ...Polynomial Division ...Polynomial and Ratio...Modeling Real-World ...Applications of Rati...Complex Numbers in E...Mastering Word Probl...Checking Your Soluti...Smart Use of Calcula...
Advanced Topics

Polynomial and Rational Inequalities

More Than Just Equal

Inequalities use \( >, <, \geq, \leq \) instead of \( = \). With polynomials and rational expressions, you find where the expression is positive or negative.

Solving Steps

  1. Set the expression to zero and find critical points (where numerator or denominator is zero).
  2. Make a sign chart to see where the expression is positive or negative.
  3. Write your solution, being careful about open and closed intervals.

Real-World Connections

Inequalities are key in fields like economics, engineering, and data science, where you want to know when something is above or below a threshold.

Examples

  • Solve \( x^2 - 4 > 0 \): \( x < -2 \) or \( x > 2 \).

  • For \( \frac{x-3}{x+2} \leq 0 \), solution is \( -2 < x \leq 3 \), \( x eq -2 \).

In a Nutshell

Polynomial and rational inequalities help us find when expressions are greater or less than a value.

Next
Modeling Real-World Data with Polynomials