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

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

Step 1

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

Move $- 4$ .

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

Move $x^{2}$ .

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

Reorder $6 x^{3}$ and $2 x^{5}$ .

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

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.

$2 x^{5} \to 5$

$6 x^{3} \to 3$

$x^{2} \to 2$

$- 4 \to 0$

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$2 x^{5}$

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.

$2 x^{5}$

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

$2$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $2 x^{5}$

Leading Coefficient: $2$