Find the Degree, Leading Term, and Leading Coefficient 5x^4+6x^9-6x^5+4x^1

$5 x^{4} + 6 x^{9} - 6 x^{5} + 4 x^{1}$

Step 1

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

Simplify.

$5 x^{4} + 6 x^{9} - 6 x^{5} + 4 x$

Move $5 x^{4}$ .

$6 x^{9} - 6 x^{5} + 5 x^{4} + 4 x$

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.

$6 x^{9} \to 9$

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

$5 x^{4} \to 4$

$4 x \to 1$

The largest exponent is the degree of the polynomial.

$9$

Step 3

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

$6 x^{9}$

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.

$6 x^{9}$

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

$6$

Step 5

List the results.

Polynomial Degree: $9$

Leading Term: $6 x^{9}$

Leading Coefficient: $6$