Find the Degree, Leading Term, and Leading Coefficient 6x-4x^4+5^7

$6 x - 4 x^{4} + 5^{7}$

Step 1

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

Raise $5$ to the power of $7$ .

$6 x - 4 x^{4} + 78125$

Reorder $6 x$ and $- 4 x^{4}$ .

$- 4 x^{4} + 6 x + 78125$

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.

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

$6 x \to 1$

$78125 \to 0$

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.

$- 4 x^{4}$

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.

$- 4 x^{4}$

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

$- 4$

Step 5

List the results.

Polynomial Degree: $4$

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

Leading Coefficient: $- 4$