Find the Degree, Leading Term, and Leading Coefficient 10x^2+x^4-5-2x^5

$10 x^{2} + x^{4} - 5 - 2 x^{5}$

Step 1

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

Move $- 5$ .

$10 x^{2} + x^{4} - 2 x^{5} - 5$

Move $10 x^{2}$ .

$x^{4} - 2 x^{5} + 10 x^{2} - 5$

Reorder $x^{4}$ and $- 2 x^{5}$ .

$- 2 x^{5} + x^{4} + 10 x^{2} - 5$

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.

$- 2 x^{5} \to 5$

$x^{4} \to 4$

$10 x^{2} \to 2$

$- 5 \to 0$

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: $- 2$