Is (-\frac{4}{9}x^4+2x-1) a polynomial?

Correct answer: Yes, because coefficients can be real and powers are valid

The direct answer is A: yes, it is a polynomial. A polynomial is an expression made from numbers and a variable in which every variable exponent is a non-negative integer: 0, 1, 2, 3, and so on. In this expression, the terms are \\(-\\frac{4}{9}x^4\\), \\(2x\\), and \\(-1\\). Their powers of x are 4, 1, and 0, respectively. The coefficients \\(-\\frac{4}{9}\\), 2, and \\(-1\\) are allowed; coefficients may be negative, fractional, or zero. Therefore the expression satisfies the definition. Option A is correct because all powers are valid and the coefficients are real numbers. Option B is wrong because a negative fraction is still a valid coefficient. Option C is wrong because \\(x^4\\) is perfectly acceptable; 4 is a non-negative integer. Option D is wrong because having three terms does not prevent an expression from being a polynomial; a polynomial may have one, two, three, or many terms. Remember: check the powers of the variable, not whether coefficients are negative or fractional and not merely how many terms appear.