The polynomial's degree is $6$.
Work Step by Step
RECALL: (1) The degree of a term is equal to the sum of the exponents of its variables. (2) The degree of a polynomial is equal to the degree of the term with the highest degree. The terms of the given polynomial have the following degrees: $-x^4$: degree = 4 $5x^3$: degree = 3 $3x^6$: degree = 6 $-1$: degree = 0 The term with the highest degree is $3x^6$. The degeree of this term is $6$. Thus, the polynomial's degree is $6$.