Find the Degree, Leading Term, and Leading Coefficient f(x)=(2x^3)/3+5/3+15x

$f (x) = \frac{2 x^{3}}{3} + \frac{5}{3} + 15 x$

Step 1

Move $\frac{5}{3}$ .

$f (x) = \frac{2 x^{3}}{3} + 15 x + \frac{5}{3}$

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.

$\frac{2 x^{3}}{3} \to 3$

$15 x \to 1$

$\frac{5}{3} \to 0$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$\frac{2 x^{3}}{3}$

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.

$\frac{2 x^{3}}{3}$

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

$\frac{2}{3}$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $\frac{2 x^{3}}{3}$

Leading Coefficient: $\frac{2}{3}$