Find the Degree, Leading Term, and Leading Coefficient 7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

$7 x^{7} + 10 x^{4} + 4 x^{3} - 5 x^{11} - 10 x^{6} - 6 x^{7}$

Step 1

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

Subtract $6 x^{7}$ from $7 x^{7}$ .

$x^{7} + 10 x^{4} + 4 x^{3} - 5 x^{11} - 10 x^{6}$

Simplify the expression.

Move $4 x^{3}$ .

$x^{7} + 10 x^{4} - 5 x^{11} - 10 x^{6} + 4 x^{3}$

Move $10 x^{4}$ .

$x^{7} - 5 x^{11} - 10 x^{6} + 10 x^{4} + 4 x^{3}$

Reorder $x^{7}$ and $- 5 x^{11}$ .

$- 5 x^{11} + x^{7} - 10 x^{6} + 10 x^{4} + 4 x^{3}$

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.

$- 5 x^{11} \to 11$

$x^{7} \to 7$

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

$10 x^{4} \to 4$

$4 x^{3} \to 3$

The largest exponent is the degree of the polynomial.

$11$

Step 3

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

$- 5 x^{11}$

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.

$- 5 x^{11}$

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

$- 5$

Step 5

List the results.

Polynomial Degree: $11$

Leading Term: $- 5 x^{11}$

Leading Coefficient: $- 5$