Answer :
Using the definition of polynomial, it is found that options D and E are polynomials.
D. [tex]4x^4 - 10[/tex]
E. [tex]15x^2 + 3x - 2[/tex]
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A polynomial of the nth degree is defined by the following equation:
[tex]p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x^1 + a_0[/tex]
The exponents n are integers, and have to be non-negative.
- In options A and C, there are negative exponents([tex]\frac{3}{5x^4} = \frac{3}{5}x^{-4})[/tex], and thus, they are not polynomials.
- In option B, [tex]\sqrt{x} = x^{\frac{1}{2}}[/tex], that is, a fractional exponent, thus also not a polynomial.
- In options D and E, the exponents are integers and non-negative, thus they are polynomials.
A similar problem is given at https://brainly.com/question/15446728