Polynomial Functions And Equations (Course Two).

This course provides a solid understanding of polynomial functions and equations, developing core algebraic skills essential for further mathematics and real-world applications in fields like engineering and finance. It establishes the properties of polynomials, which behave analogously to integers in that they are closed under addition, subtraction, and multiplication. The course focuses on mastering the operations necessary to manipulate, simplify, and solve polynomial expressions, functions and equations.

In this case, lecture one and two describe how to add and subtract two or more polynomial functions in horizontal and vertical format. The lecture gives examples on how to add or subtract polynomials (polynomials of the same degree can be added or subtracted depending on the requirement of the question). This is not true for multiplication and division. The horizontal and vertical formats are also applicable for multiplication of polynomials (the multiplication is performed between two functions one at a time). We make use of special product patterns to help in simplifying the task encountered in multiplication of polynomials.

Division of polynomials by a divisor (both long division and synthetic division method) is extensively covered in this course because it forms the backbone under which the remainder theorem is explicitly defined. Also, the lectures deeply involved areas of rational root theorem and factor theorem for solving the possible zeros and factors of a given polynomial functions and equations. Pascal's triangle and Factor theorem are broadly treated with examples for easy understanding of expansion and remainder theorem. Also, special patterns are included in lecture one. The same privilege is given to the synthetic method of division with some examples which make our lectures unique so that attending this course is a guarantee to master polynomial functions and equations , course two.

Proceeding lectures include how to find the solutions of the functions. Importance of rational root theorem with examples to buttress our points is extensively used in lecture three together with irrational conjugate theorem. This leads us to the fundamental theorem of algebra in lecture four. Descartes' rule of sign is used to determine how many real and imaginary roots a given polynomial function and equation has.

Each lecture has a quiz to test your understanding of all you learnt in subsequent lectures.