Question

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial $\text{(a)}-5\text{(b)}8y^3-7y^2-y-3\text{(c)}-3x^{2}y-5xy+9x{y}^3\text{(d)}81m^2-4n^2\text{(e)}-3x^6{y}^{3}z$

Short answer

The result will be

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& -5& \text{Monomial}& \text{0}\\ b)& 8y^3-7y^2-y-3& \text{Polynomial}& \text{3}\\ c)& -3x^{2}y-5xy+9x{y}^3& \text{Trinomial}& \text{4}\\ d)& 81m^2-4n^2& \text{Binomial}& \text{2}\\ e)& -3x^6{y}^{3}z& \text{Monomial}& \text{10}\end{array}$

Step-by-step solution

Step 1. Given information

The given polynomials are

$$\begin{gathered} \text{(a)}-5 \\ \text{(b)}8y^3-7y^2-y-3 \\ \text{(c)}-3x^{2}y-5xy+9x{y}^3 \\ \text{(d)}81m^2-4n^2 \\ \text{(e)}-3x^6{y}^{3}z \end{gathered}$$

We have to determine whether each polynomial is a monomial, binomial, trinomial, or other polynomials.

Also, we have to determine the degree of each polynomial.

Step 2. Determine the number of terms

$\begin{array}{cccc}& \text{Polynomial}& \begin{array}{l}\text{Numberof}\\ \text{terms}\end{array}& \text{Type}\\ a)& -5& 1& \text{Monomial}\\ b)& 8y^3-7y^2-y-3& 4& \text{Polynomial}\\ c)& -3x^{2}y-5xy+9x{y}^3& 3& \text{Trinomial}\\ d)& 81m^2-4n^2& 2& \text{Binomial}\\ e)& -3x^6{y}^{3}z& 1& \text{Monomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \begin{array}{l}\text{Degreeof}\\ \text{terms}\end{array}& \text{Degree}\\ a)& -5& 0& \text{0}\\ b)& 8y^3-7y^2-y-3& 3,2,1,0& \text{3}\\ c)& -3x^{2}y-5xy+9x{y}^3& 3,2,4& \text{4}\\ d)& 81m^2-4n^2& 2,2& \text{2}\\ e)& -3x^6{y}^{3}z& 10& \text{10}\end{array}$