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

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

Step 1

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

Combine $x^{3}$ and $\frac{1}{7}$ .

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

Move $1$ .

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

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.

$- \frac{x^{3}}{7} \to 3$

$10 x^{2} \to 2$

$1 \to 0$

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.

$- \frac{x^{3}}{7}$

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.

$- \frac{x^{3}}{7}$

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

$- \frac{1}{7}$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $- \frac{x^{3}}{7}$

Leading Coefficient: $- \frac{1}{7}$