Find the Degree, Leading Term, and Leading Coefficient 5x^5+3-x^2-1/5x^3

$5 x^{5} + 3 - x^{2} - \frac{1}{5} x^{3}$

Step 1

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

Combine $x^{3}$ and $\frac{1}{5}$ .

$5 x^{5} + 3 - x^{2} - \frac{x^{3}}{5}$

Reorder.

Move $3$ .

$5 x^{5} - x^{2} - \frac{x^{3}}{5} + 3$

Move $- x^{2}$ .

$5 x^{5} - \frac{x^{3}}{5} - x^{2} + 3$

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.

$5 x^{5} \to 5$

$- \frac{x^{3}}{5} \to 3$

$- x^{2} \to 2$

$3 \to 0$

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.

$5 x^{5}$

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.

$5 x^{5}$

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

$5$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $5 x^{5}$

Leading Coefficient: $5$