which algebraic expression is a polynomial with a degree of 2?\n$4x^{3}-2x$\n$10x^{2}-sqrt{x}$\n$8x^{3}+\frac…

Explanation:

Step1: Recall polynomial degree definition

The degree of a polynomial is the highest - power of the variable in the polynomial. A polynomial in one variable (x) is 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_n\neq0), and (n) is the degree.

Step2: Analyze each option

• For (4x^3-2x), the highest power of (x) is (3), so its degree is (3).
• For (10x^2-\sqrt{x}=10x^2 - x^{\frac{1}{2}}), since it has a non - integer power of (x) ((\frac{1}{2})), it is not a polynomial.
• For (8x^3+\frac{5}{x}+3 = 8x^3+5x^{- 1}+3), since it has a negative power of (x) ((-1)), it is not a polynomial.
• For (6x^2-6x + 5), the highest power of (x) is (2), and it is in the form of a polynomial (ax^2+bx + c) ((a = 6), (b=-6), (c = 5)).

Answer:

(6x^2-6x + 5)