Intermediate Algebra
I. Polynomials
a. Basic Operations with Monomials and Polynomials
1. Add, subtract, and multiply monomials and polynomials
2. Divide a polynomial by a monomial or binomial, where the quotient has no remainder
b. Factoring Trinomials
1. With a leading coefficient of 1
2. With a leading coefficient ‚ 1
c. Algebraic Fractions
1. Simplifying Algebraic Fractions
2. Multiplying and Dividing Algebraic Fractions
3. Adding and Subtracting Algebraic Fractions
4. Rationalizing Denominators
5. Simplifying Complex Fractions
II. Functions
a. Definition of a Relation
b. Definition of a Function
c. Evaluating Functions
d. Domain and Range of a Function
i. Interval Notation
e. Definition of an Inverse Function
f. Composition of Functions
III. Solving Algebraically
a. Linear Equations and Inequalities
b. Absolute Value Equations and Inequalities
c. Radicals
i. Simplifying Radical Expressions
ii. Adding, Subtracting, Multiplying and Dividing Radical Expressions
iii. Rationalizing Denominators
iv. Solving Radical Equations
d. Quadratics
i. Solve by Factoring
ii. Solve by Using the Quadratic Formula
iii. Use of the Discriminant
e. Exponential Equations
i. Graphing Exponential Equations with bases between greater than 0 and less than 1 and bases
greater than 1
ii. Applications of Exponential Equations
iii. Solving Exponential Equations with the Same Base
iv. Solving Exponential Equations with Powers of the Same Base (including negative exponents)
IV. Complex Number System
a. The Number i
b. Powers of i
c. Multiplying and Diving Complex Numbers (including conjugates)
d. Adding and Subtracting Complex Numbers
e. Solving Quadratics with Complex Roots
f. Graphing Complex Numbers
