Q. 8 - Intermediate Algebra

Question

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

$\begin{array}{l}\left(a\right)15xy\\ \left(b\right)15\\ \left(c\right)6x^2-3xy+4x-2y+y^2\\ \left(d\right)10p-9q\\ \left(e\right)m^4+4m^3+6m^2+4m+1\end{array}$

Step-by-Step Solution

Answer

The type and degree of the polynomials is 

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 15xy& \text{Monomial}& \text{2}\\ b)& 15& \text{Monomial}& \text{0}\\ c)& 6x^2-3xy+4x-2y+y^2& \text{Polynomial}& \text{2}\\ d)& 10p-9q& \text{Binomial}& \text{1}\\ e)& -m^4+4m^3+6m^2+4m+1& \text{Polynomial}& \text{4}\end{array}$

Step 1. Given information

The given polynomial expressions are 

$\begin{array}{l}\left(a\right)15xy\\ \left(b\right)15\\ \left(c\right)6x^2-3xy+4x-2y+y^2\\ \left(d\right)10p-9q\\ \left(e\right)m^4+4m^3+6m^2+4m+1\end{array}$

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

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 15xy& 1& \text{Monomial}\\ b)& 15& 1& \text{Monomial}\\ c)& 6x^2-3xy+4x-2y+y^2& 5& \text{Polynomial}\\ d)& 10p-9q& 2& \text{Binomial}\\ e)& -m^4+4m^3+6m^2+4m+1& 5& \text{Polynomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& 15xy& 2& \text{2}\\ b)& 15& 0& \text{0}\\ c)& 6x^2-3xy+4x-2y+y^2& 2,2,1,1,2& \text{2}\\ d)& 10p-9q& 1,1& \text{1}\\ e)& -m^4+4m^3+6m^2+4m+1& 4,3,2,1,0& \text{4}\end{array}$