Understanding Polynomials

The video tutorial explains polynomials as expressions involving sums of products of constants and variables with nonnegative integer exponents. It provides an example polynomial and breaks it down into terms, discussing the degree and coefficient of each term. The concept of the leading term is introduced, and the degree of the polynomial is explained. Finally, the tutorial demonstrates how to write polynomials in descending order of degree.

What is a polynomial?

• An equation with only one term.

• An expression involving a sum of products of constants and variables with nonnegative integer exponents.

• A constant number.

• A single variable raised to a power.

Which of the following is an example of a polynomial?

• 9Y + 7Y^3 - 5 - 4Y^2

• 9Y + 7Y^3 - 5 - 4Y^-2

• 9Y + 7Y^3 - 5 - 4Y^0.5

• 9Y + 7Y^3 - 5 - 4Y^1.5

What is the degree of the term 9Y in the polynomial?

• 1

• 0

• 3

• 2

What is the coefficient of the term 7Y^3?

• 0

• 9

• 7

• 3

What is the degree of the term -5 in the polynomial?

• 2

• 3

• 1

• 0

Which term is the leading term in the polynomial 9Y + 7Y^3 - 5 - 4Y^2?

• 9Y

• -4Y^2

• 7Y^3

• -5

What is the degree of the polynomial 9Y + 7Y^3 - 5 - 4Y^2?

• 1

• 4

• 2

• 3

What is the significance of the leading term in a polynomial?

• It has the lowest degree.

• It determines the degree of the polynomial.

• It is always a constant.

• It is the last term in the polynomial.

How should the polynomial 9Y + 7Y^3 - 5 - 4Y^2 be written in descending order?

• 7Y^3 + 9Y - 4Y^2 - 5

• 9Y + 7Y^3 - 5 - 4Y^2

• 7Y^3 - 4Y^2 + 9Y - 5

• -5 + 9Y - 4Y^2 + 7Y^3

What is the next topic after writing polynomials in descending order?

• Polynomials with three variables

• Polynomials with one variable

• Polynomials with two variables

• Polynomials with no variables