Find the Degree, Leading Term, and Leading Coefficient 3.75x^5-7.25x^7+9.5-6.75x^6

$3.75 x^{5} - 7.25 x^{7} + 9.5 - 6.75 x^{6}$

Step 1

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

Move $9.5$ .

$3.75 x^{5} - 7.25 x^{7} - 6.75 x^{6} + 9.5$

Move $3.75 x^{5}$ .

$- 7.25 x^{7} - 6.75 x^{6} + 3.75 x^{5} + 9.5$

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.

$- 7.25 x^{7} \to 7$

$- 6.75 x^{6} \to 6$

$3.75 x^{5} \to 5$

$9.5 \to 0$

The largest exponent is the degree of the polynomial.

$7$

Step 3

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

$- 7.25 x^{7}$

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.

$- 7.25 x^{7}$

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

$- 7.25$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $- 7.25 x^{7}$

Leading Coefficient: $- 7.25$