Find the Degree, Leading Term, and Leading Coefficient f(x)=13-2x^2+6x-9x^3

$f (x) = 13 - 2 x^{2} + 6 x - 9 x^{3}$

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

Move $13$ .

$f (x) = - 2 x^{2} + 6 x - 9 x^{3} + 13$

Move $6 x$ .

$f (x) = - 2 x^{2} - 9 x^{3} + 6 x + 13$

Reorder $- 2 x^{2}$ and $- 9 x^{3}$ .

$f (x) = - 9 x^{3} - 2 x^{2} + 6 x + 13$

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.

$- 9 x^{3} \to 3$

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

$6 x \to 1$

$13 \to 0$

The largest exponent is the degree of the polynomial.

$3$

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

$- 9 x^{3}$

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.

$- 9 x^{3}$

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

$- 9$

List the results.

Polynomial Degree: $3$

Leading Term: $- 9 x^{3}$

Leading Coefficient: $- 9$