Find the Degree, Leading Term, and Leading Coefficient -3x^4+7x-1/5-x^3

$- 3 x^{4} + 7 x - \frac{1}{5} - x^{3}$

Step 1

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

Move $- \frac{1}{5}$ .

$- 3 x^{4} + 7 x - x^{3} - \frac{1}{5}$

Move $7 x$ .

$- 3 x^{4} - x^{3} + 7 x - \frac{1}{5}$

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.

$- 3 x^{4} \to 4$

$- x^{3} \to 3$

$7 x \to 1$

$- \frac{1}{5} \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$- 3 x^{4}$

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.

$- 3 x^{4}$

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

$- 3$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $- 3 x^{4}$

Leading Coefficient: $- 3$