Find the Degree, Leading Term, and Leading Coefficient -10x^6-2x^5+4x^4+7x^3-9x^2+5.5x-1

$- 10 x^{6} - 2 x^{5} + 4 x^{4} + 7 x^{3} - 9 x^{2} + 5.5 x - 1$

Step 1

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.

$- 10 x^{6} \to 6$

$- 2 x^{5} \to 5$

$4 x^{4} \to 4$

$7 x^{3} \to 3$

$- 9 x^{2} \to 2$

$5.5 x \to 1$

$- 1 \to 0$

The largest exponent is the degree of the polynomial.

$6$

Step 2

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

$- 10 x^{6}$

Step 3

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.

$- 10 x^{6}$

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

$- 10$

Step 4

List the results.

Polynomial Degree: $6$

Leading Term: $- 10 x^{6}$

Leading Coefficient: $- 10$