Option a: ![4x^{3} -\frac{2}{x}](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20-%5Cfrac%7B2%7D%7Bx%7D)
Option b: ![2y^{3} +5y^{2} -5y](https://tex.z-dn.net/?f=2y%5E%7B3%7D%20%2B5y%5E%7B2%7D%20-5y)
Option c: ![3y^{3} -\sqrt{4y}](https://tex.z-dn.net/?f=3y%5E%7B3%7D%20-%5Csqrt%7B4y%7D)
Explanation:
The highest degree of a polynomial is the largest exponent of that variable.
Now, we shall determine the polynomial with degree 3.
Option a: ![4x^{3} -\frac{2}{x}](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20-%5Cfrac%7B2%7D%7Bx%7D)
From the expression
, the highest degree of the polynomial is 3.
Hence,
is a polynomial with a degree of 3.
Hence, Option a is the correct answer.
Option b: ![2y^{3} +5y^{2} -5y](https://tex.z-dn.net/?f=2y%5E%7B3%7D%20%2B5y%5E%7B2%7D%20-5y)
From the expression
, the highest degree of the polynomial is 3.
Hence,
is a polynomial with a degree of 3.
Hence, Option b is the correct answer.
Option c: ![3y^{3} -\sqrt{4y}](https://tex.z-dn.net/?f=3y%5E%7B3%7D%20-%5Csqrt%7B4y%7D)
From the expression
, the highest degree of the polynomial is 3.
Hence,
is a polynomial with a degree of 3.
Hence, Option c is the correct answer.
Option d: ![-xy\sqrt{6}](https://tex.z-dn.net/?f=-xy%5Csqrt%7B6%7D)
From the expression
, the highest degree of the polynomial is 1.
Hence,
is a polynomial with degree 1.
Hence, Option d is not the correct answer.