Find the Degree, Leading Term, and Leading Coefficient p(x)=3x+x^7-7x^6

$p (x) = 3 x + x^{7} - 7 x^{6}$

Step 1

Move $3 x$ .

$p (x) = x^{7} - 7 x^{6} + 3 x$

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.

$x^{7} \to 7$

$- 7 x^{6} \to 6$

$3 x \to 1$

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.

$x^{7}$

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.

$x^{7}$

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

$1$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $x^{7}$

Leading Coefficient: $1$