Find the Degree, Leading Term, and Leading Coefficient -8x^3-x^4+1/9+x

$- 8 x^{3} - x^{4} + \frac{1}{9} + x$

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Move $\frac{1}{9}$ .

$- 8 x^{3} - x^{4} + x + \frac{1}{9}$

Reorder $- 8 x^{3}$ and $- x^{4}$ .

$- x^{4} - 8 x^{3} + x + \frac{1}{9}$

The degree of a polynomial is the highest degree of its terms.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- x^{4} \to 4$

$- 8 x^{3} \to 3$

$x \to 1$

$\frac{1}{9} \to 0$

The largest exponent is the degree of the polynomial.

$4$

The leading term in a polynomial is the term with the highest degree.

$- x^{4}$

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$- x^{4}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$- 1$

List the results.

Polynomial Degree: $4$

Leading Term: $- x^{4}$

Leading Coefficient: $- 1$