which algebraic expression is a polynomial with a degree of 3?\n$4x^{3}-\frac{2}{x}$\n$2y^{3}+5y^{2}-5y$\n$3y…

Explanation:

Step1: Recall polynomial definition

A polynomial in one - variable is an expression of the form (a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0), where (n) is a non - negative integer and (a_i) are constants. Also, the degree of a polynomial is the highest power of the variable.

Step2: Analyze the first option

For the expression (4x^3-\frac{2}{x}=4x^3 - 2x^{-1}), since it has a negative exponent, it is not a polynomial.

Step3: Analyze the second option

The expression (2y^3+5y^2 - 5y) is a polynomial. The highest power of the variable (y) is 3, so its degree is 3.

Step4: Analyze the third option

For the expression (3y^3-\sqrt{4y}=3y^3 - 2y^{\frac{1}{2}}), since it has a non - integer exponent, it is not a polynomial.

Step5: Analyze the fourth option

The expression (-xy\sqrt{6}) has degree (1 + 1=2) (sum of exponents of (x) and (y)), so it is not a degree - 3 polynomial.

Answer:

(2y^3+5y^2 - 5y)