Chapter 4: Polynomials, Cubic Equations and Partial Fractions

This set of flashcards covers key concepts and definitions related to polynomials, cubic equations, and algebraic fractions as discussed in the lecture notes.

Polynomial

An algebraic expression consisting of variables and coefficients, arranged in descending powers.

Coefficient

A numerical factor in a term of an algebraic expression.

Degree of a Polynomial

The highest power of the variable in a polynomial.

Evaluate

To calculate the value of a polynomial for a specific value of the variable.

Remainder Theorem

A theorem that states the remainder of a polynomial division by (x-a) is equal to f(a).

Factor Theorem

States that (x-a) is a factor of a polynomial if and only if f(a) = 0.

Synthetic Division

A simplified method of dividing a polynomial by a binomial.

Long Division of Polynomials

A method used to divide polynomials similar to numerical long division.

Algebraic Fraction

A fraction in which the numerator and denominator are polynomials.

Proper Algebraic Fraction

An algebraic fraction where the degree of the numerator is less than the degree of the denominator.

Improper Algebraic Fraction

An algebraic fraction where the degree of the numerator is greater than or equal to the degree of the denominator.

Partial Fractions

Expression of a single algebraic fraction as the sum of two or more simpler fractions.

Cubic Equation

An equation of the form ax³ + bx² + cx + d = 0, where a, b, c, d are constants.

Real Roots

The solutions of a polynomial equation that are real numbers.

Turning Points

Points on a graph where the function changes direction, indicating local maxima or minima.