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

$2 x + 10 x^{2} - x^{3}$

Step 1

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

Move $2 x$ .

$10 x^{2} - x^{3} + 2 x$

Reorder $10 x^{2}$ and $- x^{3}$ .

$- x^{3} + 10 x^{2} + 2 x$

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.

$- x^{3} \to 3$

$10 x^{2} \to 2$

$2 x \to 1$

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.

$- x^{3}$

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.

$- x^{3}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $- x^{3}$

Leading Coefficient: $- 1$