Find the Degree, Leading Term, and Leading Coefficient x^5+2x^6-3x^4-8x+4x^3

$x^{5} + 2 x^{6} - 3 x^{4} - 8 x + 4 x^{3}$

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

Move $- 8 x$ .

$x^{5} + 2 x^{6} - 3 x^{4} + 4 x^{3} - 8 x$

Reorder $x^{5}$ and $2 x^{6}$ .

$2 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - 8 x$

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.

$2 x^{6} \to 6$

$x^{5} \to 5$

$- 3 x^{4} \to 4$

$4 x^{3} \to 3$

$- 8 x \to 1$

The largest exponent is the degree of the polynomial.

$6$

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

$2 x^{6}$

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.

$2 x^{6}$

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

$2$

List the results.

Polynomial Degree: $6$

Leading Term: $2 x^{6}$

Leading Coefficient: $2$