Q. 5 - Intermediate Algebra

Question

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

$\begin{array}{l}\left(a\right)5a^2+12ab-7b^2\\ \left(b\right)18x{y}^{2}z\\ \left(c\right)5x+2\\ \left(d\right)y^3-8y^2+2y-16\\ \left(e\right)-24\end{array}$

Step-by-Step Solution

Answer

The type and degree of the polynomials is 

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 5a^2+12ab-7b^2& \text{Trinomial}& \text{2}\\ b)& 18x{y}^{2}z& \text{Monomial}& \text{4}\\ c)& 5x+2& \text{Binomial}& \text{1}\\ d)& y^3-8y^2+2y-16& \text{Polynomial}& \text{3}\\ e)& -24& \text{Monomial}& \text{0}\end{array}$

Step 1. Given information

The given polynomial expressions are 

$\begin{array}{l}\left(a\right)5a^2+12ab-7b^2\\ \left(b\right)18x{y}^{2}z\\ \left(c\right)5x+2\\ \left(d\right)y^3-8y^2+2y-16\\ \left(e\right)-24\end{array}$

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

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 5a^2+12ab-7b^2& 3& \text{Trinomial}\\ b)& 18x{y}^{2}z& 1& \text{Monomial}\\ c)& 5x+2& 2& \text{Binomial}\\ d)& y^3-8y^2+2y-16& 4& \text{Polynomial}\\ e)& -24& 1& \text{Monomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& 5a^2+12ab-7b^2& 2,2,2& \text{2}\\ b)& 18x{y}^{2}z& 4& \text{4}\\ c)& 5x+2& 1,0& \text{1}\\ d)& y^3-8y^2+2y-16& 3,2,1,0& \text{3}\\ e)& -24& 0& \text{0}\end{array}$