Question

Which algebraic expressions are polynomials? Check all that apply.

A) πx - √3 + 5y
B) x^2y^2 - 4x^3 + 12y
C) (4/x) - x^2 - 16
D) 3.9x^3 - 4.1x^2 + 7.3

Answer 1

The algebraic expressions that are polynomials are A) πx - √3 + 5y, B) x^2y^2 - 4x^3 + 12y, and D) 3.9x^3 - 4.1x^2 + 7.3, as they all have variables raised to non-negative integer exponents and no variables in the denominator.

Step-by-step explanation:

The student has asked which algebraic expressions are polynomials. To be classified as a polynomial, an expression must be made up of terms consisting of coefficients and variables that have non-negative integer exponents, and it should not have variables in the denominator. Now, let's analyze the given expressions:

• A) πx - √3 + 5y: This is a polynomial since it consists of terms with variables raised to the first power (which are positive integers) and constants.
• B) x^2y^2 - 4x^3 + 12y: This is also a polynomial because all the variables are raised to non-negative integer powers and there are no denominators that contain variables.
• C) (4/x) - x^2 - 16: This is not a polynomial because it has a term with a variable in the denominator (4/x).
• D) 3.9x^3 - 4.1x^2 + 7.3: This is a polynomial, composed of terms with variables raised to non-negative integer exponents.

So, the expressions that are polynomials are options A, B, and D.