Find the Degree, Leading Term, and Leading Coefficient 3x^2-2+4x^8-x

$3 x^{2} - 2 + 4 x^{8} - x$

Step 1

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

Move $- 2$ .

$3 x^{2} + 4 x^{8} - x - 2$

Reorder $3 x^{2}$ and $4 x^{8}$ .

$4 x^{8} + 3 x^{2} - x - 2$

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.

$4 x^{8} \to 8$

$3 x^{2} \to 2$

$- x \to 1$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$8$

Step 3

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

$4 x^{8}$

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.

$4 x^{8}$

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

$4$

Step 5

List the results.

Polynomial Degree: $8$

Leading Term: $4 x^{8}$

Leading Coefficient: $4$