Find the Degree, Leading Term, and Leading Coefficient x^2y-7xy+xyz+x

$x^{2} y - 7 x y + x y z + x$

Step 1

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

Move $- 7 x y$ .

$x^{2} y + x y z - 7 x y + x$

Reorder $x^{2} y$ and $x y z$ .

$x y z + x^{2} y - 7 x y + x$

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.

$x y z \to 3$

$x^{2} y \to 3$

$- 7 x y \to 2$

$x \to 1$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$x y z$

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.

$x y z$

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

$1$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $x y z$

Leading Coefficient: $1$