Find the Degree, Leading Term, and Leading Coefficient 1-1/3x^3-5x^4-10x

$1 - \frac{1}{3} x^{3} - 5 x^{4} - 10 x$

Step 1

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

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

$1 - \frac{x^{3}}{3} - 5 x^{4} - 10 x$

Simplify the expression.

Move $1$ .

$- \frac{x^{3}}{3} - 5 x^{4} - 10 x + 1$

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

$- 5 x^{4} - \frac{x^{3}}{3} - 10 x + 1$

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.

$- 5 x^{4} \to 4$

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

$- 10 x \to 1$

$1 \to 0$

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.

$- 5 x^{4}$

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.

$- 5 x^{4}$

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

$- 5$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $- 5 x^{4}$

Leading Coefficient: $- 5$