Understanding Polynomials and Their Properties

The video tutorial covers the basics of polynomials, including definitions, qualifications, and standard forms. It explains how to classify polynomials by degree and number of terms, and provides practice examples. The tutorial also demonstrates operations such as addition, subtraction, and multiplication of polynomials, emphasizing the importance of correct processes and organization.

What is a monomial?

• A product of a number and one or more variables

• A polynomial with two terms

• A polynomial with three terms

• A sum of variables

Which of the following is NOT a requirement for a polynomial?

• Positive integer exponents

• Real number coefficients

• Negative integer exponents

• Variables with non-negative exponents

Why is the expression \( \sqrt{x} \) not considered a polynomial?

• It has a complex coefficient

• It has a variable in the denominator

• It has a fractional exponent

• It has a negative exponent

What does the standard form of a polynomial function involve?

• Arranging terms alphabetically

• Arranging terms by degree in ascending order

• Arranging terms by coefficient size

• Arranging terms by degree in descending order

What is the leading coefficient of a polynomial?

• The first coefficient in the polynomial

• The sum of all coefficients

• The coefficient of the term with the largest exponent

• The coefficient of the term with the smallest exponent

How do you find the y-intercept of a polynomial?

• Find the term with the highest degree

• Set the polynomial equal to zero

• Set all variables to zero and solve for the constant term

• Find the term with the lowest degree

What is a polynomial with a degree of 4 called?

• Quintic

• Quartic

• Cubic

• Quadratic

How would you classify a polynomial with three terms?

• Quadrinomial

• Trinomial

• Binomial

• Monomial

What is the leading coefficient of the polynomial \(9x^2 + 3x + 5\)?

• 5

• 2

• 9

• 3

When adding polynomials, what should you do with terms that have the same degree?

• Ignore them

• Multiply their coefficients

• Divide their coefficients

• Add or subtract their coefficients