Find the Degree, Leading Term, and Leading Coefficient 1/5a^3-3/5a^2+4/5a

$\frac{1}{5} a^{3} - \frac{3}{5} a^{2} + \frac{4}{5} a$

Step 1

Simplify each term.

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

$\frac{a^{3}}{5} - \frac{3}{5} a^{2} + \frac{4}{5} a$

Combine $a^{2}$ and $\frac{3}{5}$ .

$\frac{a^{3}}{5} - \frac{a^{2} \cdot 3}{5} + \frac{4}{5} a$

Move $3$ to the left of $a^{2}$ .

$\frac{a^{3}}{5} - \frac{3 \cdot a^{2}}{5} + \frac{4}{5} a$

Combine $\frac{4}{5}$ and $a$ .

$\frac{a^{3}}{5} - \frac{3 a^{2}}{5} + \frac{4 a}{5}$

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.

$\frac{a^{3}}{5} \to 3$

$- \frac{3 a^{2}}{5} \to 2$

$\frac{4 a}{5} \to 1$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$\frac{a^{3}}{5}$

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.

$\frac{a^{3}}{5}$

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

$\frac{1}{5}$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $\frac{a^{3}}{5}$

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