Find the Degree, Leading Term, and Leading Coefficient f(x)=-x^5-9x^2-10x^3-4x^4-10

$f (x) = - x^{5} - 9 x^{2} - 10 x^{3} - 4 x^{4} - 10$

Step 1

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

Move $- 9 x^{2}$ .

$f (x) = - x^{5} - 10 x^{3} - 4 x^{4} - 9 x^{2} - 10$

Move $- 10 x^{3}$ .

$f (x) = - x^{5} - 4 x^{4} - 10 x^{3} - 9 x^{2} - 10$

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.

$- x^{5} \to 5$

$- 4 x^{4} \to 4$

$- 10 x^{3} \to 3$

$- 9 x^{2} \to 2$

$- 10 \to 0$

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$- x^{5}$

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.

$- x^{5}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- x^{5}$

Leading Coefficient: $- 1$