Find the Degree, Leading Term, and Leading Coefficient 7x^4+3x^7-2x^8+7

$7 x^{4} + 3 x^{7} - 2 x^{8} + 7$

Step 1

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

Move $7 x^{4}$ .

$3 x^{7} - 2 x^{8} + 7 x^{4} + 7$

Reorder $3 x^{7}$ and $- 2 x^{8}$ .

$- 2 x^{8} + 3 x^{7} + 7 x^{4} + 7$

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.

$- 2 x^{8} \to 8$

$3 x^{7} \to 7$

$7 x^{4} \to 4$

$7 \to 0$

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.

$- 2 x^{8}$

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.

$- 2 x^{8}$

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

$- 2$

Step 5

List the results.

Polynomial Degree: $8$

Leading Term: $- 2 x^{8}$

Leading Coefficient: $- 2$