Find the Degree, Leading Term, and Leading Coefficient -x^5+3-10x^2-1/7x

$- x^{5} + 3 - 10 x^{2} - \frac{1}{7} x$

Step 1

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

Combine $x$ and $\frac{1}{7}$ .

$- x^{5} + 3 - 10 x^{2} - \frac{x}{7}$

Move $3$ .

$- x^{5} - 10 x^{2} - \frac{x}{7} + 3$

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.

$- x^{5} \to 5$

$- 10 x^{2} \to 2$

$- \frac{x}{7} \to 1$

$3 \to 0$

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$- x^{5}$

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.

$- x^{5}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- x^{5}$

Leading Coefficient: $- 1$