Question

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. f(x) = -16x5 - 7x4 - 6

A. Degree: -16; leading coefficient: 5
B. Degree: 5; leading coefficient: -16
C. Not a polynomial function.
D. Degree: 9; leading coefficient: -16

Answer 1

Explanation:

Part of the definition of a polynomial is that the exponents have to be non-negative integers. In other words, it cannot have a fraction as an exponent or an imaginary number. Our polynomial has real non-negative exponents, so it is in fact a polynomial. The degree is found in the highest exponent of the polynomial. Ours is a 5th degree. The leading coefficient is the number stuck to the x that has the highest degree. Therefore, our leading coefficient is -16. B is your choice.