Understanding Polynomials

The video introduces polynomials, explaining their structure and terminology. It distinguishes between polynomials and non-polynomials, focusing on the importance of non-negative exponents. The video covers key terms like degree and coefficient, and explains the standard form of polynomials. It demonstrates operations such as addition and simplification, and concludes with examples of constructing polynomials to represent areas.

What is a polynomial?

• An expression with variables raised to negative exponents

• An expression with only constant terms

• An expression with variables raised to non-negative exponents

• An expression with variables raised to any exponent

Which of the following is a binomial?

• x^(-1/2) + 1

• 4x^3 - 2^2 + 7

• y√y - y^2

• x^2 + 1

Why is x^(-1/2) + 1 not considered a polynomial?

• It has a constant term

• It has a negative exponent

• It has a fractional exponent

• It has both negative and fractional exponents

What is the degree of the polynomial 4x^3 - 2x^2 + 7?

• 1

• 2

• 4

• 3

What is the coefficient of the x^2 term in the polynomial x^2 - 5x + 7x^5 - 5?

• 5

• 7

• 1

• -5

How should terms be arranged in the standard form of a polynomial?

• In ascending order of degree

• In descending order of degree

• In alphabetical order

• In random order

What is the result of adding the polynomials -2x^2 + 4x - 12 and 7x + x^2?

• -x^2 + 11x - 12

• x^2 + 3x - 12

• x^2 + 11x - 12

• -x^2 + 3x - 12

In the expression 2a^2b - 3ab^2 + 5a^2b^2, what is the coefficient of the ab^2 term?

• 5

• 0

• -3

• 2

What is the area of a rectangle with dimensions x and y?

• x + y

• x - y

• x/y

• xy

How can the area of a shape be represented using polynomials?

• By adding the lengths of all sides

• By adding the areas of individual sections

• By multiplying the lengths of all sides

• By subtracting the areas of individual sections