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

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

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

Combine $x^{5}$ and $\frac{1}{10}$ .

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

Simplify the expression.

Move $- 1$ .

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

Reorder $x^{4}$ and $- \frac{x^{5}}{10}$ .

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

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.

$- \frac{x^{5}}{10} \to 5$

$x^{4} \to 4$

$- 1 \to 0$

The largest exponent is the degree of the polynomial.

$5$

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

$- \frac{x^{5}}{10}$

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.

$- \frac{x^{5}}{10}$

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

$- \frac{1}{10}$

List the results.

Polynomial Degree: $5$

Leading Term: $- \frac{x^{5}}{10}$

Leading Coefficient: $- \frac{1}{10}$