f(x) = a_0x^n + a_1x^(n-1)+...+a_n is said to be a polynomial of degree n (provided a_0 ≠ 0), where a_i are constants and n is a positive integer.
Thus D. x -√6 is a polynomial of degree 1.

Answer #3 | 28/12 2013 22:12

D) a polynomial is a sum of integer powers of x (positive or zero to be exact).
√6 is just a constant (i.e. x⁰) so is still a polynomial term.
The others are not:
A: 1/√x is x^(-1/2) <-- negative AND not an integer
B: 1/x = x⁻¹ <-- negative exponents are not polynomial
C: √x = x^(1/2) <-- not an integer exponent

Answer #4 | 28/12 2013 22:22

Answer D
A) is ruled out because it has both a variable to fractional power as well as a negative power
B) is ruled out because it has a negative power
C) is ruled out because it has a variable with a fractional power
D) however is ok because the fractional power [√(6)x⁰] is on the coefficient (6) not the variable x⁰

Answer #1| 28/12 2013 22:07