It means that the value of the function, f(x), is negative when x = 0.
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Yes, it can. Constants can be both positive and negative numbers.
equilibrium constant
Both terms in the binomial have positive exponents of x and so it is not possible for there to be a constant term in its expansion. If the second term is a negative power then it is not possible to tell whether it should be (a/x^2) or 1/(ax^2) which will yield different answers.
yes
In an arithmetic sequence, the difference between any term and the previous term is a constant.