Find the Degree, Leading Term, and Leading Coefficient g(x)=1/4x^3-12x+9

$g (x) = \frac{1}{4} x^{3} - 12 x + 9$

Step 1

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

$g (x) = \frac{x^{3}}{4} - 12 x + 9$

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.

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

$- 12 x \to 1$

$9 \to 0$

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: $\frac{1}{4}$