For polynomials you need to remember that they have 2 things: terms and positive exponents.
1) is not polynomial because if you rewrite it the second term has a negative exponent ( -4x^-2)
2)is a polynomial
3) is a polynomial
4) is not a polynomial because if you convert the sqrt in a exponent you have a rational exponent (4x)^1/2
5) for standard form arrange the terms from the high to low degrees
X^11 -9x^7. +4x^5. -6
The degree is 11 the leading coefficient is 1
6) same idea as 5. The degree is 6 and leading coefficient is -2
7) degree 3 and has 3 terms
8) degree 2 and has 3 terms
