Q. 6 - Intermediate Algebra

Question

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

$$\begin{gathered} \left(a\right)9y^3-10y^2+2y-6 \\ \left(b\right)-12p^{3}q \\ \left(c\right)a^2+9ab+18b^2 \\ \left(d\right)20x^2{y}^2-10a^2{b}^2+30 \\ \left(e\right)17 \end{gathered}$$

Step-by-Step Solution

Answer

The type and degree of the polynomials is 

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 9y^3-10y^2+2y-6& \text{Polynomial}& \text{3}\\ b)& -12p^{3}q& \text{Monomial}& \text{4}\\ c)& a^2+9ab+18b^2& \text{Trinomial}& \text{2}\\ d)& 20x^2{y}^2-10a^2{b}^2+30& \text{Trinomial}& \text{4}\\ e)& 17& \text{Monomial}& \text{0}\end{array}$

Step 1. Given information

The given expression are

$\begin{array}{l}\left(a\right)9y^3-10y^2+2y-6\\ \left(b\right)-12p^{3}q\\ \left(c\right)a^2+9ab+18b^2\\ \left(d\right)20x^2{y}^2-10a^2{b}^2+30\\ \left(e\right)17\end{array}$

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

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 9y^3-10y^2+2y-6& 4& \text{Polynomial}\\ b)& -12p^{3}q& 1& \text{Monomial}\\ c)& a^2+9ab+18b^2& 3& \text{Trinomial}\\ d)& 20x^2{y}^2-10a^2{b}^2+30& 3& \text{Trinomial}\\ e)& 17& 1& \text{Monomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& 9y^3-10y^2+2y-6& 3,2,1,0& \text{3}\\ b)& -12p^{3}q& 4& \text{4}\\ c)& a^2+9ab+18b^2& 2,2,2& \text{2}\\ d)& 20x^2{y}^2-10a^2{b}^2+30& 4,4,0& \text{4}\\ e)& 17& 0& \text{0}\end{array}$