Question

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.

$\begin{array}{l}\left(a\right)47x^5-17x^2{y}^3+y^2\\ \left(b\right)5c^3+11c^2-c-8\\ \left(c\right)\frac{5}{9}ab+\frac{1}{3}b\\ \left(d\right)4\\ \left(e\right)4pq+17\end{array}$

Short answer

The type of the polynomials is $\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 47x^5-17x^2{y}^3+y^2& \text{Trinomial}& 5\\ b)& 5c^3+11c^2-c-8& \text{Polynomial}& 3\\ c)& \frac{5}{9}ab+\frac{1}{3}b& \text{Binomial}& 2\\ d)& 4& \text{Monomial}& 0\\ e)& 4pq+17& \text{Binomial}& 2\end{array}$$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 47x^5-17x^2{y}^3+y^2& \text{Trinomial}& 5\\ b)& 5c^3+11c^2-c-8& \text{Polynomial}& 3\\ c)& \frac{5}{9}ab+\frac{1}{3}b& \text{Binomial}& 2\\ d)& 4& \text{Monomial}& 0\\ e)& 4pq+17& \text{Binomial}& 2\end{array}$

Step-by-step solution

Step 1. Given information

The polynomial expressions given are

$\begin{array}{l}\left(a\right)47x^5-17x^2{y}^3+y^2\\ \left(b\right)5c^3+11c^2-c-8\\ \left(c\right)\frac{5}{9}ab+\frac{1}{3}b\\ \left(d\right)4\\ \left(e\right)4pq+17\end{array}$

Step 2. Determine the type of the polynomial

$\begin{array}{cccc}& \text{Polynomial}& \text{Numberofterms}& \text{Type}\\ a)& 47x^5-17x^2{y}^3+y^2& 3& \text{Trinomial}\\ b)& 5c^3+11c^2-c-8& 4& \text{Polynomial}\\ c)& \frac{5}{9}ab+\frac{1}{3}b& 2& \text{Binomial}\\ d)& 4& 1& \text{Monomial}\\ e)& 4pq+17& 2& \text{Binomial}\end{array}$

Step 3. Determine the degree of the polynomial

$\begin{array}{cccc}& \text{Polynomial}& \text{Degreeofterms}& \text{Degree}\\ a)& 47x^5-17x^2{y}^3+y^2& 5,5,2& \text{5}\\ b)& 5c^3+11c^2-c-8& 3,2,1,0& \text{3}\\ c)& \frac{5}{9}ab+\frac{1}{3}b& 2,1& \text{2}\\ d)& 4& 0& \text{0}\\ e)& 4pq+17& 2& \text{2}\end{array}$