Exploring Polynomials and Their Vocabulary

This video tutorial covers the basics of adding and subtracting polynomials. It begins with a review of key vocabulary, including expressions, monomials, binomials, and trinomials. The video then explains polynomials, their classification, and how to determine their degree. It also covers writing polynomials in standard form and identifying the leading coefficient. The tutorial includes practice problems and demonstrates two methods for adding polynomials: horizontal and vertical formats.

What is an expression in mathematics?

• A math sentence with numbers only

• A math sentence with variables only

• A math sentence without an equal sign

• A math sentence with an equal sign

Which of the following is a binomial?

• 5x

• x^2 + 3x + 4

• x^2 - 7

• 4 + 3

What is a polynomial?

• An expression with one or more terms

• An expression with one term

• An expression with three terms

• An expression with two terms

How do you classify a polynomial by its degree?

• By the term with the smallest exponent

• By the number of terms it has

• By the number of variables it has

• By the term with the greatest exponent

What is the leading coefficient of the polynomial 2x^3 - x^2 + 4x - 8?

• -8

• 4

• -1

• 2

Which of the following is the correct standard form of the polynomial -x^4 + 3x^2 + 1?

• 1 + 3x^2 - x^4

• -x^4 + 3x^2 + 1

• -x^4 + 1 + 3x^2

• 3x^2 - x^4 + 1

What are like terms?

• Terms with the same variables and exponents

• Terms with different exponents

• Terms with different variables

• Terms with the same coefficients

How do you add polynomials using the horizontal format?

• Write each term in a separate column

• Combine unlike terms and write them in a single line

• Write each term in a separate line

• Combine like terms and write them in a single line

What is the result of adding the polynomials 3x^2 - 7x + 2 and -x^2 + 4x + 5?

• 2x^2 - 3x + 7

• 4x^2 - 3x + 7

• 2x^2 - 3x + 3

• 2x^2 + 3x + 7

In the vertical format, where should you place the terms of the second polynomial?

• Below the terms of the first polynomial

• Above the terms of the first polynomial

• In a separate column

• Next to the terms of the first polynomial