Find the Degree, Leading Term, and Leading Coefficient 3x^4+6x-1/2x^3-1

$3 x^{4} + 6 x - \frac{1}{2} x^{3} - 1$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Combine $x^{3}$ and $\frac{1}{2}$ .

$3 x^{4} + 6 x - \frac{x^{3}}{2} - 1$

Move $6 x$ .

$3 x^{4} - \frac{x^{3}}{2} + 6 x - 1$

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.

$3 x^{4} \to 4$

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

$6 x \to 1$

$- 1 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$3 x^{4}$

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.

$3 x^{4}$

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

$3$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $3 x^{4}$

Leading Coefficient: $3$