polynomials
A polynomial expression is a fundamental concept in algebra, which consists of a combination of monomials that are added or subtracted to form the expression. A monomial is essentially a single term that comprises a constant, a variable, or a product of both, for example, \( a x^n \). A polynomial, therefore, has the form: \[ a_n x^n + a_{n-1} x^{n-1} + \cdots + a_2 x^2 + a_1 x + a_0 \]
A polynomial is an algebraic expression containing sums and differences of monomials.
Ruffini’s rule provides a systematic and efficient method for polynomial division, which leads to a rapid factorization of polynomials and the solution of equations of degree \(n > 2\).
Rational equations feature at least one fraction in which the numerator and denominator are polynomials.They have the form:
\[P(x) \over Q(x)\]
The parabola is a plane curve defined as the set of all points that are equidistant from a fixed point \(F \) called the focus, and a fixed line \( d \) called the directrix.
A circumference is the set of all points in a plane that are at a fixed distance from a given point, called the center. The equation of the circumference is:
\[
(x – x_0)^2 + (y – y_0)^2 = r^2
\]
A series with positive terms is a series in which all the terms are greater than zero.
The Cauchy theorem states that, under certain conditions of continuity and differentiability for two functions \( f(x) \) and \( g(x) \), there exists at least one point in the interval where the ratio of their derivatives equals the ratio of their increments at the endpoints of the interval.
\[
\frac{f’ \left(c \right)}{g’ \left(c \right)} = \frac{f(b) – f(a)}{g(b) – g(a)}
\]