# Polynomial Functions

## Contents

#### Terms

Asymptote  -  A line that a function approaches but never intersects.
Axis  -  The line of symmetry of a parabola.
Constant Function  -  A polynomial function of degree zero in which the constant term ≠ 0 .
Constant Term  -  The coefficient of x 0 in a polynomial.
Degree  -  The value of n in a polynomial f (x) = a n x n + a n-1 x n-1 + ... + a 1 x + a 0 , where a n≠ 0 . If f (x) = 0 , then the degree is undefined.
Descartes' Rule of Signs  -  Descartes' Rule of Signs states that the number of positive real roots is less than or equal to the number of variations in the function f (x) . It also states that the number of negative real roots is less than or equal to the number of variations in the function f (- x) .
Leading Coefficient  -  The value of a n in a polynomial f (x) = a n x n + a n-1 x n-1 + ... + a 1 x + a 0 , where a n≠ 0 unless f (x) = 0 .
Linear Function  -  A first-degree polynomial.
Multiplicity  -  If (x - c)n is a factor of a polynomial but (x - c)n+1 is not, the root c is said to be a root of multiplicity n .
Parabola  -  Another name for the graph of a quadratic function.
Polynomial  -  An expression of one variable of the form a n x n + a n-1 x n-1 + ... + a 2 x 2 + a 1 x + a 0 , where a n, a n-1,..., a 1, a 0 are real numbers, n is a nonnegative integer, and a n≠ 0 .
Polynomial Function  -  A function that is defined by a polynomial; it is of the form f (x) = a n x n + a n-1 x n-1 + ... + a 2 x 2 + a 1 x + a 0 , where a n, a n-1,…, a 1, a 0 are real numbers, n is a nonnegative integer, and a n≠ 0 .
Quadratic Function  -  A second-degree polynomial.
Rational Function  -  A function which can be expressed as the quotient of two polynomial functions.
Rational Root Theorem  -  The Rational Root Theorem is a useful tool in finding the roots of a polynomial function f (x) = a n x n + a n-1 x n-1 + ... + a 2 x 2 + a 1 x + a 0. If the coefficients of a polynomial are all integers, and a root of the polynomial is rational (it can be expressed as a fraction in lowest terms), the Rational Root Theorem states that the numerator of the root is a factor of a 0 and the denominator of the root is a factor of a n .
Root  -  Values of the independent variable for which a polynomial function equals zero.
Variation  -  Consecutive terms of a polynomial whose coefficients have opposite signs.
Vertex  -  The point on a parabola at which the quadratic function reaches its minimum or maximum value.
Zero Polynomial  -  The polynomial f (x) = 0 .

#### Formulae

 Quadratic Formula If ax 2 + bx + c = 0 , then x = .