Find the Degree, Leading Term, and Leading Coefficient (x^5)/5+1-x^4+9x^2

$\frac{x^{5}}{5} + 1 - x^{4} + 9 x^{2}$

Step 1

Move $1$ .

$\frac{x^{5}}{5} - x^{4} + 9 x^{2} + 1$

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.

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

$- x^{4} \to 4$

$9 x^{2} \to 2$

$1 \to 0$

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.

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

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.

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

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

$\frac{1}{5}$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $\frac{x^{5}}{5}$

Leading Coefficient: $\frac{1}{5}$