A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a...

This lecture explains a procedure used to divide polynomials that is analogous to the procedure used to divide integers called "long division". Dividing one polynomial (the dividend) by another (the divisor) produces a quotient that may...

In the previous lecture we saw how polynomial functions could be added or subtracted, producing new polynomial functions with different characteristics. In this lecture we will see how to multiply polynomial functions and show how the...

Adding polynomial functions produces another polynomial function. The values of this function are the sum of the values of the polynomials that were added for every possible value of the input variable(s). Fortunately, adding polynomial...

When sketching the graph of a polynomial function, it may not be necessary to calculate numerous points on the graph. Many clues as to the general shape of the graph can be derived if we understand the characteristics that the graphs of...

Calculators and graphing utilities are available that are capable of creating accurate graphs of polynomial functions. However, it is often desirable to sketch a quick representation of a function's graph to get a general idea of its...

A polynomial is a sum of one or more terms called monomials. If we think of each monomial as a separate function, then a polynomial function can be thought of as a sum of these monomial functions. In previous lectures we have studied...

A video entitled “Factor Polynomials” which models how to factor quadratic equations.

In this lesson, students will learn how to subtract polynomials by using the distributive property and combining like terms. They will discover that the difference of two polynomials is still a polynomial, as long as the exponents are...

This video discusses the limitations of using zeros to graph a quadratic function and introduces the concept of functions with no zeros or real roots. It explains that if a quadratic function has no real number values that make it equal...

This video will teach how to rewrite common functional expressions into a "derivative friendly" form. A good understanding of intermediate algebra is required to succeed in any calculus class.

In this video, the teacher explains the concept of closed operations for polynomials. They demonstrate how addition, subtraction, and multiplication of integers and natural numbers result in solutions that are still within the same set....

It explains zero, constant and one variable polynomial with activity and numerical. Describes types of polynomials on the basis of number of terms.

In this lesson, students will learn how to describe the end behavior of polynomial and exponential functions. They will understand that for polynomial functions, the end behavior is determined by the leading term, while for exponential...

Learn that by using signed number operations and aligning like terms, you can easily add the coefficients of each pair of terms. The video emphasizes that addition of numbers with negative signs can be written in either order. Overall,...

In this video lesson, students learn how to multiply complex numbers using the definition of i and the procedures for multiplying polynomials. The lesson covers multiplying polynomials with multiple terms by a polynomial with one term,...

In this lesson, students will learn how to determine which of two polynomial functions eventually exceeds the other by comparing their degrees. By understanding the end behavior of polynomial functions and analyzing the leading terms,...

👉 Learn how to find and write the equation of the tangent line of a curve at a given point. The tangent of a curve at a point is a line that touches the circumference of the curve at that point. To find the equation of the tangent line...

In this video, the teacher explains how to find the zeros of a quadratic function by factoring a trinomial. They explain the zero product property and the importance of factoring completely. They then demonstrate how to apply these...

In this video, we explore the concept of end behavior in polynomials. We learn that the behavior of a polynomial as x approaches positive or negative infinity depends on the degree and leading coefficient of the polynomial. We examine...

In this video, the teacher explains how to find zeros of polynomial equations by factoring and using the zero product property. They demonstrate the process with examples, breaking down the steps and showing how to determine the correct...

In this video, the teacher explains how to find the zeros of a polynomial function using a graphing calculator. They demonstrate the process of long division to determine factors and use the quadratic formula to solve quadratic...

Interpolation constructs new prediction points from a discrete set of known data points. There are many types of interpolation such as nearest neighbor (piecewise constant), linear, polynomial, cubic spline, and basis spline. In...

Solutions to Problem 28.