Classifying Polynomials: Key Concepts and Techniques

Mr. Lee introduces polynomials, explaining their definitions, terms, and types, such as monomials, binomials, and trinomials. He discusses the degree and leading coefficient of polynomials and provides examples of non-polynomial expressions. The video also covers how to identify polynomial features and arrange them in standard form.

Which of the following is an example of a monomial?

• 5x^3

• 1/y^2

• x^2 - 4

• x^2 - 4x + 1

What must be true for an expression to be considered a monomial?

• It must have at least two terms.

• It must include a fraction.

• All exponents must be positive.

• It must have a variable in the denominator.

What is the term used to describe each separate monomial in a polynomial?

• Term

• Exponent

• Coefficient

• Degree

What is the degree of a polynomial?

• The highest exponent in the polynomial.

• The number of terms in the polynomial.

• The number in front of the highest degree term.

• The sum of all exponents in the polynomial.

Which of the following is a binomial?

• 1/y^2

• x^2 - 4x + 1

• 5x^3

• x^2 - 4

Which of the following is NOT a polynomial?

• x^2 - 4x + 1

• x^2 - 4

• y√x - 4x^-3 + 17

• 5x^3

How many terms does a trinomial have?

• One

• Two

• Four

• Three

What is the leading coefficient of the polynomial 4x^5 + 3x^2 - 7x?

• 3

• 7

• 4

• 5

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

• 4

• 5

• 3

• 2

In standard form, how is a polynomial written?

• From lowest degree to highest degree.

• In numerical order of coefficients.

• From highest degree to lowest degree.

• In alphabetical order of variables.