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Answer #1
In mathematics, a polynomial is an expression of finite length
constructed from variables (also called indeterminates) and
constants, using only the operations of addition, subtraction,
multiplication, and non-negative integer exponents. However, the
division by a constant is allowed, because the multiplicative
inverse of a non zero constant is also a constant. For example, x2
- x/4 + 7 is a polynomial, but x2 - 4/x + 7x3/2 is not, because its
second term involves division by the variable x (4/x), and also
because its third term contains an exponent that is not a
non-negative integer (3/2). The term "polynomial" can also be used
as an adjective, for quantities that can be expressed as a
polynomial of some parameter, as in polynomial time, which is used
in computational complexity theory.
Polynomial comes from the Greek poly, "many" and medieval Latin
binomium, "binomial". The word was introduced in Latin by
Franciscus Vieta.[4]
Polynomials appear in a wide variety of areas of mathematics and
science. For example, they are used to form polynomial equations,
which encode a wide range of problems, from elementary word
problems to complicated problems in the sciences; they are used to
define polynomial functions, which appear in settings ranging from
basic chemistry and physics to economics and social science; they
are used in calculus and numerical analysis to approximate other
functions. In advanced mathematics, polynomials are used to
construct polynomial rings, a central concept in abstract algebra
and algebraic geometry.