Course Overview

MTH 95 – Intermediate Algebra is a foundational college-level course designed to deepen students’ understanding of algebraic concepts and prepare them for advanced mathematics. The course covers a range of topics essential for success in mathematics, science, and related fields.

Student Learning Outcomes

• Classify polynomials and find proper factorizations.

• Evaluate, simplify, and solve radical expressions or equations, including those with complex numbers.

• Solve quadratic equations using different techniques.

• Simplify and solve rational expressions or equations.

Course Outline

Week 1: Review of Polynomial Multiplication and Factoring Basics

• Polynomial Multiplication: Review rules of exponents, distributive property, and FOIL method.

• Factors & GCF: Identifying factors and finding the greatest common factor (GCF).

Week 2: Factoring Trinomials

• Factoring Trinomials: Techniques for factoring expressions of the form .

• Factoring by Grouping: Using grouping to factor more complex trinomials.

• Factoring Using FOIL: Applying the FOIL method in reverse to factor trinomials.

Week 3: Special Factoring Forms and Quadratic Equations

• Special Factoring Forms: Recognizing and factoring perfect square trinomials, difference of squares, and sum/difference of cubes.

• General Approach to Factoring: Step-by-step strategies for factoring any polynomial.

• Solve Quadratic Equations by Factoring: Setting expressions to zero and solving for variable values.

Week 4: Rational Expressions

• Multiply & Divide Rational Expressions: Simplifying and operating with rational expressions.

Week 5: Rational Expressions (Continued)

• Add & Subtract Rational Expressions: Finding common denominators and combining expressions.

• Simplify Complex Rational Expressions: Reducing complex fractions to simplest form.

• Solve Rational Equations: Solving equations involving rational expressions.

Week 6: Radical Expressions and Rational Exponents

• Rational Exponents: Understanding and simplifying expressions with fractional exponents.

• Simplify Radical Expressions: Reducing radicals to simplest form.

• Adding & Subtracting Radical Expressions: Combining like radicals.

Week 7: Operations with Radicals and Complex Numbers

• Multiply & Divide Radical Expressions: Applying multiplication and division rules to radicals.

• Solve Radical Equations: Isolating and solving equations with radicals.

• Complex Numbers: Introduction to numbers of the form .

Week 8: Quadratic Equations – Advanced Methods

• Solve Quadratics: Square Root Property: Solving equations by taking square roots.

• Solve Quadratics: Complete the Square: Transforming equations to perfect square form.

Week 9: Quadratic Formula and Graphs

• Solve Quadratics: Quadratic Formula: Using the formula to solve any quadratic equation.

• Equations in Quadratic Form: Recognizing and solving equations that can be rewritten as quadratics.

• Graphs of Quadratic Functions (Intro): Basic properties and shapes of parabolas.

Week 10: Basic Graphing and Review

• Basic Graphing: Plotting and interpreting graphs of algebraic functions.

• Review: Comprehensive review of all course topics in preparation for the final exam.

Key Concepts and Definitions

• Polynomial: An algebraic expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

• Factoring: The process of expressing a polynomial as a product of its factors.

• Rational Expression: A fraction in which the numerator and/or denominator are polynomials.

• Radical Expression: An expression containing a root, such as a square root or cube root.

• Quadratic Equation: An equation of the form .

• Complex Number: A number in the form , where is the imaginary unit ().

Grading and Course Policies

• Homework: 20 points, completed on MyMathLab, with late penalties.

• Quizzes: 20 points, two attempts per quiz, late penalties apply.

• Exams: 60 points, including two midterms and a comprehensive final, proctored online.

• No extra credit or extensions except by prior arrangement.

Required Materials

• Inclusive Access: All course materials are provided digitally via MyMathLab and Canvas.

Academic Integrity and Conduct

• Plagiarism and Cheating: Strictly prohibited; see Student Handbook for definitions and consequences.

• Classroom Behavior: Respectful, non-disruptive conduct is required. Cell phones must be off during lectures.

• Disability Accommodations: Contact Accessible Education Office for support.

• Non-Discrimination: The college does not discriminate based on protected status; see syllabus for details.

Example: Factoring a Trinomial

To factor , find two numbers that multiply to 6 and add to 5. These are 2 and 3, so:

Example: Solving a Quadratic Equation Using the Quadratic Formula

Given , apply the quadratic formula:

So or .

Additional Information

• Students are expected to spend at least two hours per credit per week on coursework outside of class.

• For grievances, class cancellations, and further policies, refer to the Student Handbook and college website.