Understanding Polynomials

This video tutorial introduces polynomials, explaining their definition and characteristics. It covers examples of polynomial and non-polynomial expressions, and defines types of polynomials such as monomials, binomials, and trinomials. The video also discusses key polynomial features like leading terms, coefficients, and degree, providing examples to illustrate these concepts.

What is a polynomial in one variable?

• A constant divided by a variable

• A variable with a negative exponent

• A constant or the product of a constant and a variable with any exponent

• A constant or the product of a constant and a variable with a non-negative integer exponent

Which of the following is a polynomial term?

• √x

• x^2

• 5/x

• x^-1

Why is 5/x not considered a polynomial?

• It is a constant term

• It has a non-negative integer exponent

• It is a quotient, not a product

• It is a product of a constant and a variable

What is a monomial?

• A polynomial with one term

• A polynomial with four terms

• A polynomial with two terms

• A polynomial with three terms

Which of the following is a binomial?

• 12x^5 - 2x^2 + x + 7

• 12x^5

• 12x^5 - 2x^2 + x

• 12x^5 + 2x^2

What is the leading term in the polynomial 12x^5 - 2x^2 + x?

• x

• 12

• 12x^5

• -2x^2

How do you determine the degree of a polynomial?

• By the number of terms it has

• By the leading coefficient

• By the constant term

• By the highest exponent on the variable

What is the constant term in the polynomial 12x^5 - 2x^2 + x - 7?

• -7

• 12

• -2

• x

Which polynomial has a degree of 3?

• 4x

• 2m^3 + 3m^2

• 24a^6 + 5

• x^3 + 2x + 1

What is the leading coefficient of the polynomial 24a^6 + 5?

• 6

• 24

• 5

• a