Find the Degree, Leading Term, and Leading Coefficient f(x)=-2x^2+4x^3+9+x^6-5x^5

$f (x) = - 2 x^{2} + 4 x^{3} + 9 + x^{6} - 5 x^{5}$

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

Move $9$ .

$f (x) = - 2 x^{2} + 4 x^{3} + x^{6} - 5 x^{5} + 9$

Move $- 2 x^{2}$ .

$f (x) = 4 x^{3} + x^{6} - 5 x^{5} - 2 x^{2} + 9$

Move $4 x^{3}$ .

$f (x) = x^{6} - 5 x^{5} + 4 x^{3} - 2 x^{2} + 9$

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.

$x^{6} \to 6$

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

$4 x^{3} \to 3$

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

$9 \to 0$

The largest exponent is the degree of the polynomial.

$6$

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

$x^{6}$

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.

$x^{6}$

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

$1$

List the results.

Polynomial Degree: $6$

Leading Term: $x^{6}$

Leading Coefficient: $1$