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

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

Step 1

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

Move $3$ .

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

Move $- 2 x^{2}$ .

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

Reorder $x^{6}$ and $4 x^{7}$ .

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

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.

$4 x^{7} \to 7$

$x^{6} \to 6$

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

$- 4 x \to 1$

$3 \to 0$

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.

$4 x^{7}$

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.

$4 x^{7}$

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

$4$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $4 x^{7}$

Leading Coefficient: $4$