Polynomials: One Variable

The video tutorial covers the basics of algebra, focusing on polynomials. It explains the definition of polynomials in one variable, their components such as terms, coefficients, and degree, and how to classify them based on the number of terms and degree. The tutorial also discusses the concept of constant and zero polynomials, and provides examples to illustrate these concepts.

What is a polynomial in one variable?

• An expression with multiple variables and whole number exponents

• An expression with one variable and whole number exponents

• An expression with one variable and fractional exponents

• An expression with multiple variables and fractional exponents

Which of the following is a term in a polynomial?

• A constant only

• An operator

• A variable only

• A combination of constants and variables

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

• 2

• 3

• 4

• 5

What is a monomial?

• A polynomial with four terms

• A polynomial with three terms

• A polynomial with two terms

• A polynomial with one term

Which of the following is a binomial?

• x^2 + x + 1

• x^3

• x^2 + 3x + 2

• x + 2

What is a linear polynomial?

• A polynomial of degree 0

• A polynomial of degree 3

• A polynomial of degree 1

• A polynomial of degree 2

What is a quadratic polynomial?

• A polynomial of degree 1

• A polynomial of degree 2

• A polynomial of degree 3

• A polynomial of degree 4

What happens if the leading coefficient of a cubic polynomial is zero?

• It remains a cubic polynomial

• It becomes a quadratic polynomial

• It becomes a linear polynomial

• It becomes a constant polynomial

What is a general polynomial?

• A polynomial with only constant terms

• A polynomial with a fixed degree

• A polynomial with a variable degree

• A polynomial with no terms

How can a general polynomial become a constant polynomial?

• If the variable is zero

• If all coefficients are zero

• If the leading coefficient is nonzero

• If the degree is zero