Exploring Polynomial Operations and Vocabulary

This video tutorial covers the basics of polynomials, including definitions and examples of monomials and polynomials. It explains how to determine the degree and leading coefficient of a polynomial and discusses different types of polynomials such as binomials and trinomials. The tutorial also provides methods for adding and subtracting polynomials, emphasizing the importance of combining like terms and arranging terms by degree.

What is a monomial?

• An algebraic expression with one term

• An algebraic expression with multiple terms

• An algebraic expression with two terms

• An algebraic expression with three terms

How do you determine the degree of a monomial?

• By multiplying the coefficients

• By adding the exponents of the variables

• By counting the number of terms

• By subtracting the exponents of the variables

Which of the following is NOT a monomial?

• 7

• 2/x

• 3y^2

• 5x

What does the term 'poly' in polynomial mean?

• One

• Two

• Three

• Multiple

How is the degree of a polynomial determined?

• By the number of variables

• By the number of terms

• By the highest degree of its terms

• By the sum of all coefficients

What is a binomial?

• A polynomial with four terms

• A polynomial with one term

• A polynomial with two terms

• A polynomial with three terms

Which of the following is a trinomial?

• x^2 + 2x + 1

• x^3

• x^2 + y^2

• x + y

What is the leading coefficient of the polynomial 3x^2 + 2x + 1?

• 0

• 2

• 3

• 1

When adding polynomials, what must be true about the terms being combined?

• They must have the same coefficients

• They must have the same variables and exponents

• They must have the same degree

• They must have the same number of terms

What happens to the signs of the terms when subtracting polynomials?

• They all become positive

• They change to the opposite sign

• They remain the same

• They all become negative