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

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

Step 1

Reorder $- 2 x^{4}$ and $3 x^{5}$ .

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

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.

$3 x^{5} \to 5$

$- 2 x^{4} \to 4$

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

$9 x^{2} \to 2$

$2 x \to 1$

$- 5 \to 0$

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.

$3 x^{5}$

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.

$3 x^{5}$

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

$3$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $3 x^{5}$

Leading Coefficient: $3$