Find the Degree, Leading Term, and Leading Coefficient 6x+5x^4-10x+8x^3-7x^2+9^2

$6 x + 5 x^{4} - 10 x + 8 x^{3} - 7 x^{2} + 9^{2}$

Step 1

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

Raise $9$ to the power of $2$ .

$6 x + 5 x^{4} - 10 x + 8 x^{3} - 7 x^{2} + 81$

Subtract $10 x$ from $6 x$ .

$5 x^{4} - 4 x + 8 x^{3} - 7 x^{2} + 81$

Move $- 4 x$ .

$5 x^{4} + 8 x^{3} - 7 x^{2} - 4 x + 81$

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.

$5 x^{4} \to 4$

$8 x^{3} \to 3$

$- 7 x^{2} \to 2$

$- 4 x \to 1$

$81 \to 0$

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: $5$