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 tutorial highlights the leading term, which has the highest degree, and explains how to write polynomials in descending order of degree. The video concludes with a brief mention of polynomials with two variables.

What is a polynomial?

• A constant number.

• A single variable raised to a power.

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

• An equation with only one term.

How many terms are in the polynomial 9Y + 7Y^3 - 5 - 4Y^2?

• Two

• Five

• Three

• Four

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

• 4

• 3

• 2

• 1

What is the coefficient of the term 9Y?

• Y

• 0

• 9

• 1

What is the coefficient of the term -4Y^2?

• 4

• -2

• 2

• -4

What is the degree of a constant term in a polynomial?

• 2

• 0

• 1

• 3

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

• 2

• 3

• 0

• 1

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

• -4Y^2

• 9Y

• 7Y^3

• -5

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

• 2

• 1

• 4

• 3

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

• 7Y^3 + 9Y - 4Y^2 - 5

• -5 + 9Y - 4Y^2 + 7Y^3

• 7Y^3 - 4Y^2 + 9Y - 5

• 9Y - 4Y^2 + 7Y^3 - 5