Find the Degree, Leading Term, and Leading Coefficient P(x)=3x^4-7x^2-2x^7-x+4

$P (x) = 3 x^{4} - 7 x^{2} - 2 x^{7} - x + 4$

Step 1

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

Move $- 7 x^{2}$ .

$P (x) = 3 x^{4} - 2 x^{7} - 7 x^{2} - x + 4$

Reorder $3 x^{4}$ and $- 2 x^{7}$ .

$P (x) = - 2 x^{7} + 3 x^{4} - 7 x^{2} - x + 4$

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.

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

$3 x^{4} \to 4$

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

$- x \to 1$

$4 \to 0$

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.

$- 2 x^{7}$

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.

$- 2 x^{7}$

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

$- 2$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $- 2 x^{7}$

Leading Coefficient: $- 2$