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

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

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

Move $- x^{2}$ .

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

Reorder $4 x^{3}$ and $- \frac{x^{5}}{9}$ .

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

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.

$- \frac{x^{5}}{9} \to 5$

$4 x^{3} \to 3$

$- x^{2} \to 2$

$5 x \to 1$

$1 \to 0$

The largest exponent is the degree of the polynomial.

$5$

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

$- \frac{x^{5}}{9}$

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.

$- \frac{x^{5}}{9}$

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

$- \frac{1}{9}$

List the results.

Polynomial Degree: $5$

Leading Term: $- \frac{x^{5}}{9}$

Leading Coefficient: $- \frac{1}{9}$