Find the Degree, Leading Term, and Leading Coefficient x^3y+2x^3+3x^2y-5x^4+7x^3y+8x+4

$x^{3} y + 2 x^{3} + 3 x^{2} y - 5 x^{4} + 7 x^{3} y + 8 x + 4$

Step 1

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

Add $x^{3} y$ and $7 x^{3} y$ .

$2 x^{3} + 3 x^{2} y - 5 x^{4} + 8 x^{3} y + 8 x + 4$

Simplify the expression.

Move $2 x^{3}$ .

$3 x^{2} y - 5 x^{4} + 8 x^{3} y + 2 x^{3} + 8 x + 4$

Move $3 x^{2} y$ .

$- 5 x^{4} + 8 x^{3} y + 3 x^{2} y + 2 x^{3} + 8 x + 4$

Reorder $- 5 x^{4}$ and $8 x^{3} y$ .

$8 x^{3} y - 5 x^{4} + 3 x^{2} y + 2 x^{3} + 8 x + 4$

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.

$8 x^{3} y \to 4$

$- 5 x^{4} \to 4$

$3 x^{2} y \to 3$

$2 x^{3} \to 3$

$8 x \to 1$

$4 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$8 x^{3} y$

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.

$8 x^{3} y$

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

$8$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $8 x^{3} y$

Leading Coefficient: $8$