Introduction

Elementary algebra is a system for talking about numbers without having to say, or even know, exactly what the numbers are. You do this by using some other symbol to stand for each number. This symbol could be anything that doesn't already have a meaning, usually a letter like x, A, or n. You can also use letters from other languages, like φ (Greek) or ℵ (Hebrew), entire words like length or population, or even nonsense symbols like ↵ or ◊. I'll mostly use ordinary English letters.

In Beginning Algebra, you should have learnt how to solve linear equations (such as 2x = 5 and 3(t + 5) = 6t − 4) and seen examples of polynomials (such as x2 + 5 and 3a3 + 5a − 8). Now we will go further and learn to solve many (although not all) polynomial equations. To solve these equations, you will need some irrational numbers, which did not really come up in Beginning Algebra: the radicals, numbers like √2 and 5 + 6 3√5. And in the course of studying polynomial equations, you will also learn about some more algebraic expressions: the rational expressions, expressions like 5/(x + 2) and (y3 − 5)/(2y2 + 3y  + 9).

You won't learn how to solve all polynomial equations; that is a very deep subject in general, which even most math majors never learn completely. However, you can learn more about them in College Algebra. College Algebra also deals heavily with the concept of functions, which we will touch on slightly.


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