Final answer:
The function given is a polynomial and in standard form, it is -3x^4 - x^3 + 2x^2 - 2x + 5. It is a fourth-degree polynomial with a leading coefficient of -3.
Step-by-step explanation:
The function given is f(x)=5+2x^2-3x^4-2x-x^3. To determine if it is a polynomial, let's check if it only contains terms with non-negative integer exponents of x and real coefficients. This function fits that definition, so it is a polynomial.
Next, we will write it in standard form, which means arranging it from highest degree to lowest degree. The standard form of the function is -3x^4 - x^3 + 2x^2 - 2x + 5. The degree of the polynomial is the highest exponent, which in this case is 4, so it's a fourth-degree polynomial or a quartic polynomial. The leading coefficient is the coefficient of the term with the highest exponent, which here is -3.