Q. 4 - Intermediate Algebra

Question

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

$\begin{array}{l}\left(a\right)11y^2\\ \left(b\right)-73\\ \left(c\right)6x^2-3xy+4x-2y+y^2\\ \left(d\right)4y^2+17z^2\\ \left(e\right)5c^3+11c^2-c-8\end{array}$

Step-by-Step Solution

Answer

The type and degree of the polynomials is 

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 11y^2& \text{Monomial}& \text{2}\\ b)& -73& \text{Monomial}& \text{0}\\ c)& 4y^2+17z^2& \text{Binomial}& \text{2}\\ d)& 81a{b}^4-24a^2{b}^2+3b& \text{Trinomial}& \text{5}\\ e)& 5c^3+11c^2-c-8& \text{Polynomial}& \text{3}\end{array}$

Step 1. Given information

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 11y^2& 1& \text{Monomial}\\ b)& -73& 1& \text{Monomial}\\ c)& 4y^2+17z^2& 2& \text{Binomial}\\ d)& 81a{b}^4-24a^2{b}^2+3b& 3& \text{Trinomial}\\ e)& 5c^3+11c^2-c-8& 4& \text{Polynomial}\end{array}$

Step 2. Determine the type

$\begin{array}{cccc}& \text{Polynomial}& \text{Number of terms}& \text{Type}\\ a)& 11y^2& 1& \text{Monomial}\\ b)& -73& 1& \text{Monomial}\\ c)& 4y^2+17z^2& 2& \text{Binomial}\\ d)& 81a{b}^4-24a^2{b}^2+3b& 3& \text{Trinomial}\\ e)& 5c^3+11c^2-c-8& 4& \text{Polynomial}\end{array}$

Step 3. Determine the degree

$\begin{array}{cccc}& \text{Polynomial}& \text{Degree of terms}& \text{Degree}\\ a)& 11y^2& 2& \text{2}\\ b)& -73& 0& \text{0}\\ c)& 4y^2+17z^2& 2,2& \text{2}\\ d)& 81a{b}^4-24a^2{b}^2+3b& 5,4,1& \text{5}\\ e)& 5c^3+11c^2-c-8& 3,2,1,0& \text{3}\end{array}$