What is the definition of a monomial and polynomials with examples

The video tutorial introduces monomials and polynomials, defining them and providing examples. Monomials are described as numbers, variables, or their products, while polynomials are sums of monomials. Examples of both are given, along with non-examples to highlight restrictions such as rational and negative powers. The tutorial emphasizes understanding what constitutes a polynomial and notes that square roots and variables in denominators are not part of polynomials.

What is a monomial?

• A quotient of two variables

• A difference of two numbers

• A product of a number and a variable

• A sum of two or more variables

Which of the following is an example of a monomial?

• 5x^2 + 3

• x + y

• 7

• x^2 - 4

What is the basic definition of a polynomial?

• A single variable

• A difference of two monomials

• A sum of two or more monomials

• A product of two numbers

Which of the following is a polynomial?

• x^3/2 - 4

• x^1/2 + 3x^2

• 2x^-3 + 5

• 3x^2 + 2x + 1

Why can't polynomials have rational powers?

• They create a complex number

• They simplify to a constant

• They result in a negative number

• They produce a root

Which of the following is NOT allowed in a polynomial?

• Negative powers

• Positive integer powers

• Variables with coefficients

• Whole number coefficients

What is a key characteristic of a polynomial?

• It can have variables in the denominator

• It can have square roots

• It must have at least three terms

• It cannot have rational or negative powers