The main thing about a polynomial is it's the sum of terms, each a constant coefficient times whole number power (0, 1, 2, 3, ...) of the variable.
A. 35x² is a polynomial; the power 2 is a whole number. There's only one term so not really the sum of terms, but one's enough.
B. [tex]4x + x \sqrt{-1} = (4+i)x[/tex]
That's a perfectly good polynomial but you might not have gotten to it in algebra I yet. The square root of negative 1 is abbreviated i and when we add it to the set of real numbers we get complex numbers. It has a complex coefficient 4+i but that's OK in a polynomial.
If you haven't gotten to complex numbers yet you might be expected to answer no to this one. I don't know.
C. [tex]7x^7 - x^{-5}[/tex]
The negative exponent means this isn't a polynomial.
D. x/5 + 2
That's fine, just another way of writing
[tex]\frac 1 5 x + 2[/tex]
which is a perfectly ok polynomial.
Answer: A B D
