Q. 3 - Intermediate Algebra

Question

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

$$\begin{gathered} \left(a\right)8y-5x \\ \left(b\right)y^2-5yz-6z^2 \\ \left(c\right)y^3-8y^2+2y-16 \\ \left(d\right)81a{b}^4-24a^2{b}^2+3b \\ \left(e\right)-18 \end{gathered}$$

Step-by-Step Solution

Answer

The type and the degree of the given expressions is 

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 8y-5x& \text{Binomial}& \text{1}\\ b)& y^2-5yz-6z^2& \text{Trinomial}& \text{2}\\ c)& y^3-8y^2+2y-16& \text{Polynomial}& \text{3}\\ d)& 81a{b}^4-24a^2{b}^2+3b& \text{Polynomial}& \text{4}\\ e)& -18& \text{Monomial}& \text{0}\end{array}$

Step 1. Given information

The given expressions are

$\begin{array}{l}\left(a\right)8y-5x\\ \left(b\right)y^2-5yz-6z^2\\ \left(c\right)y^3-8y^2+2y-16\\ \left(d\right)81a{b}^4-24a^2{b}^2+3b\\ \left(e\right)-18\end{array}$

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

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 8y-5x& 2& \text{Binomial}\\ b)& y^2-5yz-6z^2& 3& \text{Trinomial}\\ c)& y^3-8y^2+2y-16& 4& \text{Polynomial}\\ d)& 81a{b}^4-24a^2{b}^2+3b& 4& \text{Polynomial}\\ e)& -18& 1& \text{Monomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& 8y-5x& 1,1& \text{1}\\ b)& y^2-5yz-6z^2& 2,2,2& \text{2}\\ c)& y^3-8y^2+2y-16& 3,2,1,0& \text{3}\\ d)& 81a{b}^4-24a^2{b}^2+3b& 5,4,1& \text{4}\\ e)& -18& 0& \text{0}\end{array}$