Understanding Polynomials

The video tutorial explains how to determine if an expression is a polynomial and categorizes it as a monomial, binomial, or trinomial. It defines a monomial as a single term that can be a number, variable, or product of both with a whole number exponent. The video also highlights conditions that disqualify an expression from being a monomial, such as having a variable in the denominator or under a radical. Through examples, it demonstrates how to analyze expressions to identify polynomials and their types, and concludes with a summary of key points.

What is a polynomial with two terms called?

• Quadrinomial

• Trinomial

• Binomial

• Monomial

Which of the following is NOT a characteristic of a monomial?

• It can have a whole number exponent.

• It can be a number.

• It can have a variable in the denominator.

• It can be a product of a number and variables.

What is the degree of a polynomial?

• The highest exponent in the polynomial.

• The coefficient of the first term.

• The sum of all exponents in the polynomial.

• The number of terms in the polynomial.

In the first example, why is the expression considered a polynomial?

• It has a variable in the denominator.

• It has a fractional exponent.

• It has a negative exponent.

• All terms have whole number exponents.

Why is the second example not a polynomial?

• It has a fractional exponent.

• It has more than three terms.

• It has a negative exponent.

• It has a variable in the denominator.

What categorizes the third example as a binomial?

• It has a variable under a radical.

• It has three terms.

• It has two terms.

• It has a variable in the denominator.

Why is the fourth example not a polynomial?

• It has a fractional exponent.

• It has a negative exponent.

• It has a variable under a radical.

• It has a variable in the denominator.

What is the issue with the fifth example?

• It has a fractional exponent.

• It has a negative exponent.

• It has a variable in the denominator.

• It has a variable under a radical.

In the sixth example, what makes it not a polynomial?

• It has a fractional exponent.

• It has a variable under a radical.

• It has a variable in the denominator.

• It has a negative exponent.

Which of the following is a valid monomial?

• 3x^(-2)

• 5x^(1/2)

• x^(1/3)

• 7x^3