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

$4 + 6 x^{7} + 10 x - 5 x^{6} - 2 x^{5}$

Step 1

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

Move $4$ .

$6 x^{7} + 10 x - 5 x^{6} - 2 x^{5} + 4$

Move $10 x$ .

$6 x^{7} - 5 x^{6} - 2 x^{5} + 10 x + 4$

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.

$6 x^{7} \to 7$

$- 5 x^{6} \to 6$

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

$10 x \to 1$

$4 \to 0$

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.

$6 x^{7}$

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.

$6 x^{7}$

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

$6$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $6 x^{7}$

Leading Coefficient: $6$