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

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

Step 1

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

Move $9$ .

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

Move $- x$ .

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

Move $- 4 x^{3}$ .

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

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.

$- 9 x^{5} \to 5$

$x^{4} \to 4$

$- 4 x^{3} \to 3$

$- x \to 1$

$9 \to 0$

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.

$- 9 x^{5}$

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.

$- 9 x^{5}$

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

$- 9$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- 9 x^{5}$

Leading Coefficient: $- 9$