Lecture Notes: Polynomials and WebAssign Overview

A set of flashcards covering WebAssign setup, course logistics, and core polynomial concepts from the lecture notes.

What steps are taken to register for WebAssign from Canvas?

Go to cengage.com, create a student account using your VT email, then return to Canvas and click on an assignment to register you for WebAssign.

Where can you find the cost policy and lecture note outlines in the course files?

In the Files section of Canvas.

What is the purpose of the lecture note outlines?

They provide the lecture notes the instructor fills in during lectures; you can download them before class.

When does the course meet and when is the recitation session scheduled?

Lectures are on Monday, Wednesday, and Friday at 10:10 AM; recitation sessions occur at a different time and may be on Mon/Wed/Fris, with no recitation this week.

What percentage of the grade does recitation attendance contribute?

5%.

How are the three tests and the final exam weighted in the course grade?

Three tests are each 15% (total 45%), and the final exam is 20%.

How much do weekly WebAssign assignments contribute to the grade?

15%.

What portion of the grade comes from weekly homework assignments?

10%.

What warning does the instructor give about the course pace?

The course moves at a very fast pace, so students should keep up with the material.

How is a polynomial defined in terms of a variable?

A polynomial is a sum of powers of a variable with nonnegative integer exponents.

What can the coefficients of a polynomial be?

Coefficients can be any real numbers; there are no restrictions on coefficients.

What is meant by the degree of a polynomial?

The highest exponent that appears in the polynomial.

Can you use variables other than x for polynomials?

Yes; you can use any variable, such as x, t, y, m, z, etc.

What is a constant polynomial and its degree?

A polynomial with no variables; its degree is 0 (e.g., 19 = 19 x^0).

Why is a term like x^(-1) not a polynomial?

Because polynomials require nonnegative integer exponents.

Why is x^(1/2) not a polynomial?

Because exponents must be nonnegative integers; 1/2 is not an integer.

What is a rational expression?

A ratio of two polynomials; it is not itself a polynomial.

What is a term in a polynomial?

An individual addend, i.e., a coefficient times a monomial.

What is a polynomial in two variables?

An expression that is a sum of terms with x^a y^b, where a and b are nonnegative integers.

Do all terms in a two-variable polynomial have to show both variables?

No; some terms may omit one or both variables, but across all terms both variables must appear at least once.

How do you determine the degree of a term in a multi-variable polynomial?

Add the exponents of all variables in that term.

How do you determine the degree of the whole polynomial in multiple variables?

Find the degree of each term and take the maximum among them.

What is the degree of the term 18 x^4 y^6?

10 (4 + 6 = 10).

What is the degree of the term 2 x y^3?

4 (1 + 3 = 4).

How do you add polynomials?

Combine like terms—terms with the same variables raised to the same powers—and add their coefficients.

How do you subtract polynomials?

Distribute the negative sign to the second polynomial or subtract coefficients term-by-term.

What is the distributive property used for in polynomial multiplication?

To multiply a term by each term in a polynomial and then add the results.

What is the rule for multiplying like bases with exponents?

Add the exponents: a^m · a^n = a^(m+n).

What is the result of multiplying 3 x^5 by (7 x^3 - 2 x^2 + 3 x - 9)?

21 x^8 - 6 x^7 + 3 x^6 - 27 x^5.

How do you multiply polynomials by distributing over multiple terms (e.g., (x+8)(x+1))?

Distribute each term in the first factor across all terms in the second; simplify to x^2 + 9x + 8.