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

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

Step 1

Move $- x^{2}$ .

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

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.

$2 x^{5} \to 5$

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

$- x^{2} \to 2$

$9 \to 0$

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.

$2 x^{5}$

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.

$2 x^{5}$

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

$2$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $2 x^{5}$

Leading Coefficient: $2$