Fundamental concepts of algebra

This chapter reviews the basic tools of algebra: numbers, exponents, roots, polynomials, and fractions with variables. You will use these tools on every page of this course.

If you took algebra in high school, much of this will be familiar. Work through the examples anyway. College courses expect you to use these skills quickly and without mistakes.

This chapter covers the following topics:

Real numbers

Kinds of numbers, decimals, the real number line and order, properties of real numbers, absolute value and distance, and interval notation.

Exponents and radicals

Integer exponents and their laws, scientific notation, square roots and other roots, simplifying radicals, and rational exponents.

Polynomials and factoring

Adding, subtracting, and multiplying polynomials, special products, and factoring by common factors, grouping, trinomials, and special patterns.

Rational expressions

Simplifying, multiplying, dividing, adding, and subtracting rational expressions, and complex fractions.

Practice questions

Practice problems on every section of this chapter, with full step-by-step solutions.