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

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

Step 1

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

Combine $x$ and $\frac{1}{9}$ .

$- \frac{x}{9} + 9 - x^{3}$

Simplify the expression.

Move $9$ .

$- \frac{x}{9} - x^{3} + 9$

Reorder $- \frac{x}{9}$ and $- x^{3}$ .

$- x^{3} - \frac{x}{9} + 9$

Step 2

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.

$- x^{3} \to 3$

$- \frac{x}{9} \to 1$

$9 \to 0$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$- x^{3}$

Step 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.

$- x^{3}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $- x^{3}$

Leading Coefficient: $- 1$