
Identification of Polynomial functions and their degree
Define power functions as y = x^n; examine how even and odd powers with positive or negative coefficients yield concave up or down graphs, and show shifts and scaling.
Master polynomial graphs by locating x-intercepts and y-intercepts, using multiplicities to determine crossing or touching, assessing end behavior and turning points, and testing intervals.
Identify how a polynomial graph behaves by analyzing factor multiplicities as even or odd, x-intercepts, and the y-intercept to determine which option matches the given graph.
apply the remainder theorem to a polynomial division, identify the dividend, quotient, and divisor, and determine p and q, then compute p plus q equals 12.
Apply the remainder theorem to f(x)=x^3−2x+a and g(x)=2x^3+x−a. Equate f(1) and g(−1/2) to solve for a, yielding a=1/8.
Apply the remainder theorem to set f(5/2) = 7 for f(x) = 4x^3 + a x^2 + 7x - 23. Solve for a and find a = -8.
explore polynomial long division by recapping numeric long division, then apply it to a dividend and divisor to determine the quotient and remainder.
Apply rational zero theorem and synthetic division to factor a quartic into linear factors, identify roots -1, 2, 1/2, and 3, and sketch the graph with end behavior and intercepts.
In the comprehensive course, students will delve into the fascinating world of polynomial function, exploring their properties, applications and real world connections.
The course focuses on identification of polynomial functions, finding the zeroes of a polynomial function, graphing of polynomial function, division of polynomial function, applying remainder theorem in finding the remainder of a polynomial function, applying factor theorem in finding the factor of a polynomial function, applying Descartes rule of sign and the rational zeroes theorem in graphing the polynomial function.
In addition to the objectives, the course helps the students to develop critical thinking and problem-solving skills through the interactive lessons and activities. The learner need to be familiar with linear and quadratic functions. Also, the learner should be conversant with long division.
The course is arranged in a format that starts with the video lessons before the downloadable materials to help the the learner in revision of the concepts taught.
The course is designed for parents whose children are still in high school, especially the ones preparing for SAT. and additional mathematics students. It is also good for mathematics educators and lovers.
The self-paced online course includes video lessons and a downloadable pdf notes attached to each video. Approximately, 3 hours, depending on the learners pace is required to cover the course.
Join us on this engaging journey into the world of polynomial function.