Algebra builds in layers, and Preliminaries is the first one: the exponent rules, radicals, polynomial arithmetic, and number-system extensions that almost every later topic quietly assumes you already have. All seven lessons in this chapter are published, each with a full properties table, worked examples, ten practice problems with hidden step-by-step answers, and real MathJax notation throughout — plus a matching practice generator for unlimited drilling once the lesson itself makes sense.
They’re deliberately ordered, not just grouped. Integer Exponents sets up the product, quotient, and power rules; Rational Exponents shows those exact same rules still hold once the exponent is a fraction; Radicals is that same idea again, written with a root sign instead. Separately, Polynomials covers combining and multiplying, Factoring Polynomials runs that multiplication backward, and Rational Expressions uses factoring to simplify fractions built from polynomials. Complex Numbers closes the chapter by reusing the radical lesson’s conjugate trick on a completely different problem: clearing an imaginary number from a denominator instead of a root.
The seven lessons
1. Integer Exponents
The product, quotient, power, zero, and negative exponent rules, derived from repeated multiplication instead of just handed to you. Read the lesson · Practice generator
2. Rational Exponents
What a fractional exponent like \(a^{1/n}\) actually means, and why every integer-exponent rule still applies unchanged. Read the lesson · Practice generator
3. Radicals
Simplifying, combining like radicals, multiplying, and rationalizing a denominator with a conjugate. Read the lesson · Practice generator
4. Polynomials
Degree, standard form, adding and subtracting, multiplying (including FOIL), and the special product patterns worth memorizing outright. Read the lesson · Practice generator
5. Factoring Polynomials
The GCF, difference of squares, perfect square trinomials, and the ac method for a leading coefficient other than 1. Read the lesson · Practice generator
6. Rational Expressions
Simplifying, multiplying, dividing, and combining fractions built from polynomials — plus why an excluded value survives even after a factor cancels. Read the lesson · Practice generator
7. Complex Numbers
The imaginary unit, the repeating power-of-\(i\) cycle, and dividing complex numbers by multiplying by the conjugate. Read the lesson · Practice generator
Where to go from here
If you’re working through the chapter for the first time, start at the top and go in order — each lesson leans on the one before it. If you already know a topic, jump straight to its practice generator and see how fast you can clear a set of Hard problems.
Browse the full Algebra chapter list, see every domain on the site at Math Lessons, or find the matching drill for any topic on the Math Practice Generators page.