Find the Degree, Leading Term, and Leading Coefficient (x^2)/5+1-x^5

$\frac{x^{2}}{5} + 1 - x^{5}$

Step 1

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

Move $1$ .

$\frac{x^{2}}{5} - x^{5} + 1$

Reorder $\frac{x^{2}}{5}$ and $- x^{5}$ .

$- x^{5} + \frac{x^{2}}{5} + 1$

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.

$- x^{5} \to 5$

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

$1 \to 0$

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.

$- x^{5}$

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.

$- x^{5}$

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

$- 1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- x^{5}$

Leading Coefficient: $- 1$