more) variables in the equation. These can further be defined as any combination of
variables or constants linked together by any operation—addition, subtraction, multi-
plication, division (except division by zero). This type of algebraic equation is often
referred to as a polynomial (see elsewhere in this chapter for more about polynomials).Who was the first mathematicianto write and solve general
algebraic equations?
French mathematician François Viète (1540–1603; also known as Franciscus Vieta) is
often referred to as the “founder of modern algebra.” He was not a professional mathe-
matician, but he contributed a great deal to the understanding and spread of modern
symbolic algebra. Although some of his work paid tribute to ancient mathematical tradi-
tions, Viète created a kind of “new math”: It was not one based on the traditional geomet-
ric visualizations, but rather expressed as abstract formulas and general rules. But Viète
still divided algebra into distinct branches partially derived from Greek mathematics:
zetetics(translating a problem into an equation), poristics(proving theorems through
equations), and exegetics(solving equations). He also was the first to combine algebra
with geometry and trigonometry. (For more about Viète, see “History of Mathematics.”)What are variablesin algebraic equations?
Variables are the symbols (usually a letter such as xor y) used in algebraic equations
that represent an unknown number—and on whose value a function, polynomial, and
so on, depends. Variables remain unknown until the equation is solved; thus, they are
sometimes referred to as unknownsin an algebraic equation.
It is not always easy to work with variables, as there are so many letters used
throughout various equations. But in many mathematical and scientific texts, there
are some variables that are customary to use. They are listed as follows:
nindicates natural numbers or integers
xrepresents real numbers
zstands for complex numbersWhat are some other termsused in dealing with algebraic equations?
There are many terms in algebra, including those dealing with equations. The follow-
ing lists some of the more common ones:
Equalityand inequality—An equality is a mathematical statement that shows the
equivalence of two quantities. For example, if ais equal to b,it is written as the equal-
ity ab. An inequality is just the opposite: adoes not equal b,or a b.
Formula—A formula is a rule, fact, or principle expressed in terms of mathemati-
134 cal symbols, including equations, equalities, identities, or inequalities. (Note: The