Find the Degree, Leading Term, and Leading Coefficient 4x^2+3xy+12yz

$4 x^{2} + 3 x y + 12 y z$

Step 1

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

Move $4 x^{2}$ .

$3 x y + 12 y z + 4 x^{2}$

Reorder $3 x y$ and $12 y z$ .

$12 y z + 3 x y + 4 x^{2}$

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.

$12 y z \to 2$

$3 x y \to 2$

$4 x^{2} \to 2$

The largest exponent is the degree of the polynomial.

$2$

Step 3

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

$12 y z$

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.

$12 y z$

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

$12$

Step 5

List the results.

Polynomial Degree: $2$

Leading Term: $12 y z$

Leading Coefficient: $12$