Find the Degree, Leading Term, and Leading Coefficient -1/9x^2-x^5-7x+3x^4+1

$- \frac{1}{9} x^{2} - x^{5} - 7 x + 3 x^{4} + 1$

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

Combine $x^{2}$ and $\frac{1}{9}$ .

$- \frac{x^{2}}{9} - x^{5} - 7 x + 3 x^{4} + 1$

Reorder.

Move $- 7 x$ .

$- \frac{x^{2}}{9} - x^{5} + 3 x^{4} - 7 x + 1$

Move $- \frac{x^{2}}{9}$ .

$- x^{5} + 3 x^{4} - \frac{x^{2}}{9} - 7 x + 1$

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.

$- x^{5} \to 5$

$3 x^{4} \to 4$

$- \frac{x^{2}}{9} \to 2$

$- 7 x \to 1$

$1 \to 0$

The largest exponent is the degree of the polynomial.

$5$

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

$- x^{5}$

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.

$- x^{5}$

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

$- 1$

List the results.

Polynomial Degree: $5$

Leading Term: $- x^{5}$

Leading Coefficient: $- 1$