Find the Degree, Leading Term, and Leading Coefficient f(x)=-8x^2+6+x^6+x

$f (x) = - 8 x^{2} + 6 + x^{6} + x$

Step 1

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

Move $6$ .

$f (x) = - 8 x^{2} + x^{6} + x + 6$

Reorder $- 8 x^{2}$ and $x^{6}$ .

$f (x) = x^{6} - 8 x^{2} + x + 6$

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.

$x^{6} \to 6$

$- 8 x^{2} \to 2$

$x \to 1$

$6 \to 0$

The largest exponent is the degree of the polynomial.

$6$

Step 3

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

$x^{6}$

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.

$x^{6}$

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

$1$

Step 5

List the results.

Polynomial Degree: $6$

Leading Term: $x^{6}$

Leading Coefficient: $1$