Polynomials
A polynomial is an expression of one variable
of the form a n x n + a n-1 x n-1 + ... + a 2x 2 + a 1 x + a 0 ,
where a n, a n-1,…, a 1, a 0 are
real numbers, n is a positive integer, and a n≠
0 . The degree of a polynomial is n . a n, a n-1,…, a 1, a 0 are
the coefficients of the polynomial. a n is the
leading coefficient, and a 0 is the constant
term. a n x n,a n-1 x n-1,…, a 2 x 2, a 1 x, a 0 are
the terms of the polynomial. There are n + 1 terms in a
polynomial of degree n .
A polynomial function is any function which is
a polynomial; that is, it is of the form f (x) = a nx n + a n-1 x n-1 + ... + a 2 x 2 + a 1 x+ a 0 .
The roots of a polynomial function are the values of x for
which the function equals zero. Roots are also known as zeros,x -intercepts,
and solutions. All of these terms are synonymous. One of the most important
things to learn about polynomials is how to find their roots.
Polynomial functions have special names
depending on their degree. A polynomial function of degree zero has only a
constant term -- no x term. If the constant is zero, that is,
if the polynomial f (x) = 0 , it is called the
zero polynomial. If the constant is not zero, then f (x)
= a 0 , and the polynomial function is called
a constant function. If the polynomial function has degree one, then it is of
the form f (x) = ax + b ,
and is called a linear function. If the polynomial is of degree two, then it is
of the form f (x) = ax 2 + bx + c ,
and is called a quadratic function. In the next section, we'll learn more about
quadratic functions.
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