Power Functions and Polynomial Functions

Question

1

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.

Degree =   

Leading Coefficient =   

Maximum number of real zeros = 

Answer 1

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.

I presume the equation is as re-typed below with the powers/exponents raised as shown.

f(x)=−5x³−x⁵−2x⁶ (typically it is rewritten in descending order: f(x) = −2x⁶ −x⁵ −5x³)

Degree =   this is asking for the highest exponent, Degree is 6

Leading Coefficient =   this is the leading coefficient associated with the highest degree, so -2

Maximum number of real zeros = is equal to the highest degree, so there are a possible 6 real zeros.