The strictest definition of a polynomial admits a sum of terms each a constant times a natural number power of the variable (or each variable), or a constant.
A. Has a [tex] \sqrt{x}[/tex], a one-half power. The exponents of x must be natural numbers. NO
B. sum of constants times natural number powers of x. YES
C. -7 isn't a natural number, this isn't a polynomial in x. It is one in 1/x but I'll still go with NO.
D. Natural powers of x and a constant, YES
E. Dividing by a function of x, not allowed. NO
F. All natural powers, YES
Answer: check B D F
