Q. 2 - Intermediate Algebra

Question

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

$\begin{array}{l}\left(a\right)x^2-y^2\\ \left(b\right)-13c^4\\ \left(c\right)a^2+2ab-7b^2\\ \left(d\right)4x^2{y}^2-3xy+8\\ \left(e\right)19\end{array}$

Step-by-Step Solution

Answer

The type and degree of the polynomials is

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& x^2-y^2& \text{Binomial}& \text{2}\\ b)& -13c^4& \text{Monomial}& \text{4}\\ c)& a^2+2ab-7b^2& \text{Trinomial}& \text{2}\\ d)& 4x^2{y}^2-3xy+8& \text{Trinomial}& \text{4}\\ e)& 19& \text{Monomial}& \text{0}\end{array}$

Step 1. Given information

The given polynomial expressions are

$\begin{array}{l}\left(a\right)x^2-y^2\\ \left(b\right)-13c^4\\ \left(c\right)a^2+2ab-7b^2\\ \left(d\right)4x^2{y}^2-3xy+8\\ \left(e\right)19\end{array}$

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 type

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& x^2-y^2& 2& \text{Binomial}\\ b)& -13c^4& 1& \text{Monomial}\\ c)& a^2+2ab-7b^2& 3& \text{Trinomial}\\ d)& 4x^2{y}^2-3xy+8& 3& \text{Trinomial}\\ e)& 19& 1& \text{Monomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& x^2-y^2& 2,2& \text{2}\\ b)& -13c^4& 4& \text{4}\\ c)& a^2+2ab-7b^2& 2,2,2& \text{2}\\ d)& 4x^2{y}^2-3xy+8& 4,2,0& \text{4}\\ e)& 19& 0& \text{0}\end{array}$