Find the Degree, Leading Term, and Leading Coefficient 16-6x^2-7x^3+5x^4

$16 - 6 x^{2} - 7 x^{3} + 5 x^{4}$

Step 1

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

Move $16$ .

$- 6 x^{2} - 7 x^{3} + 5 x^{4} + 16$

Move $- 6 x^{2}$ .

$- 7 x^{3} + 5 x^{4} - 6 x^{2} + 16$

Reorder $- 7 x^{3}$ and $5 x^{4}$ .

$5 x^{4} - 7 x^{3} - 6 x^{2} + 16$

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.

$5 x^{4} \to 4$

$- 7 x^{3} \to 3$

$- 6 x^{2} \to 2$

$16 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$5 x^{4}$

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.

$5 x^{4}$

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

$5$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $5 x^{4}$

Leading Coefficient: $5$