Find the Degree, Leading Term, and Leading Coefficient 1/3x^5+x^2-x-10+3x^3

$\frac{1}{3} x^{5} + x^{2} - x - 10 + 3 x^{3}$

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

Combine $\frac{1}{3}$ and $x^{5}$ .

$\frac{x^{5}}{3} + x^{2} - x - 10 + 3 x^{3}$

Reorder.

Move $- 10$ .

$\frac{x^{5}}{3} + x^{2} - x + 3 x^{3} - 10$

Move $- x$ .

$\frac{x^{5}}{3} + x^{2} + 3 x^{3} - x - 10$

Move $x^{2}$ .

$\frac{x^{5}}{3} + 3 x^{3} + x^{2} - x - 10$

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.

$\frac{x^{5}}{3} \to 5$

$3 x^{3} \to 3$

$x^{2} \to 2$

$- x \to 1$

$- 10 \to 0$

The largest exponent is the degree of the polynomial.

$5$

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

$\frac{x^{5}}{3}$

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.

$\frac{x^{5}}{3}$

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

$\frac{1}{3}$

List the results.

Polynomial Degree: $5$

Leading Term: $\frac{x^{5}}{3}$

Leading Coefficient: $\frac{1}{3}$