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

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

Step 1

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

Move $9$ .

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

Move $- 2 x$ .

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

Move $- x^{2}$ .

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

Step 2

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.

$- x^{4} \to 4$

$- x^{3} \to 3$

$- x^{2} \to 2$

$- 2 x \to 1$

$9 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$- x^{4}$

Step 4

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.

$- x^{4}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $- x^{4}$

Leading Coefficient: $- 1$