Find the Degree, Leading Term, and Leading Coefficient 7x^6-6x^5+2x^3+x-8

$7 x^{6} - 6 x^{5} + 2 x^{3} + x - 8$

Step 1

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.

$7 x^{6} \to 6$

$- 6 x^{5} \to 5$

$2 x^{3} \to 3$

$x \to 1$

$- 8 \to 0$

The largest exponent is the degree of the polynomial.

$6$

Step 2

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

$7 x^{6}$

Step 3

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.

$7 x^{6}$

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

$7$

Step 4

List the results.

Polynomial Degree: $6$

Leading Term: $7 x^{6}$

Leading Coefficient: $7$