Q. 7 - Intermediate Algebra

Question

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

$\begin{array}{l}\left(a\right)14s-29t\\ \left(b\right)z^2-5z-6\\ \left(c\right)y^3-8y^{2}z+2y{z}^2-16z^3\\ \left(d\right)23a{b}^2-14\\ \left(e\right)-3\end{array}$

Step-by-Step Solution

Answer

The type and degree of the polynomials is $\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 14s-29t& \text{Binomial}& \text{1}\\ b)& z^2-5z-6& \text{Trinomial}& \text{2}\\ c)& y^3-8y^{2}z+2y{z}^2-16z^3& \text{Polynomial}& \text{3}\\ d)& 23a{b}^2-14& \text{Binomial}& \text{3}\\ e)& -3& \text{Monomial}& \text{0}\end{array}$

Step 1. Given information

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 14s-29t& 2& \text{Binomial}\\ b)& z^2-5z-6& 3& \text{Trinomial}\\ c)& y^3-8y^{2}z+2y{z}^2-16z^3& 4& \text{polynomial}\\ d)& 23a{b}^2-14& 2& \text{Binomial}\\ e)& -3& 1& \text{Monomial}\end{array}$

Step 2. Determine the type

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& 14s-29t& 1,1& \text{1}\\ b)& z^2-5z-6& 2,1,0& \text{2}\\ c)& y^3-8y^{2}z+2y{z}^2-16z^3& 3,3,3,3& \text{3}\\ d)& 23a{b}^2-14& 3,0& \text{3}\\ e)& -3& 0& \text{0}\end{array}$