Question

(a) Is it a monomial, binomial, or trinomial?

(b) What is its degree?

$\left(15x{y}^3-35x^{2}y\right)÷5xy$

Short answer

The given polynomial is a binomial of degree 2.

Step-by-step solution

Step 1. Given Information

• The given polynomial is$\left(15x{y}^3-35x^{2}y\right)÷5xy$

Part (a) Step 1. Count the Terms in Simplified Polynomial 

• Simplify the polynomial as follows:

$\begin{array}{rcl}\frac{{\displaystyle \left(15x{y}^3-35x^{2}y\right)}}{5xy}& =& \frac{15x{y}^3}{5xy}-\frac{35x^{2}y}{5xy}\\ & =& 3y^2-7x\end{array}$

• As the simplified polynomial has 2 terms, it is a binomial.

Part (b) Step 1. Find the Highest Power 

• The term with the highest power of the variables is $3y^2$and its exponent is 2.
• So, the degree of the binomial is 2.