Find the Degree, Leading Term, and Leading Coefficient g(x)=-1/4x^3-4x+8

$g (x) = - \frac{1}{4} x^{3} - 4 x + 8$

Step 1

Combine $x^{3}$ and $\frac{1}{4}$ .

$g (x) = - \frac{x^{3}}{4} - 4 x + 8$

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.

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

$- 4 x \to 1$

$8 \to 0$

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.

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

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.

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

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

$- \frac{1}{4}$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $- \frac{x^{3}}{4}$

Leading Coefficient: $- \frac{1}{4}$