Question

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial

$\text{(a)}64k^3-8\text{(b)}9m^3+4m^2-2\text{(c)}\frac{5}{6}\text{(d)}8a^4-7a^{3}b-6a^2{b}^2-4a{b}^3+7b^4\text{(e)}-p^4{q}^3$

Short answer

The result will be

$\begin{array}{cccc}& \text{Polynomial}& \text{Type}& \text{Degree}\\ a)& 64k^3-8& \text{Binomial}& \text{3}\\ b)& 9m^3+4m^2-2& \text{Trinomial}& \text{3}\\ c)& \frac{5}{6}& \text{Monomial}& \text{0}\\ d)& 8a^4-7a^{3}b-6a^2{b}^2-4a{b}^3+7b^4& \text{Polynomial}& \text{4}\\ e)& -p^4{q}^3& \text{Monomial}& \text{7}\end{array}$

Step-by-step solution

Step 1. Given information

$\begin{array}{cccc}& \text{Polynomial}& \begin{array}{l}\text{Numberof}\\ \text{terms}\end{array}& \text{Type}\\ a)& 64k^3-8& 2& \text{Binomial}\\ b)& 9m^3+4m^2-2& 3& \text{Trinomial}\\ c)& \frac{5}{6}& 1& \text{Monomial}\\ d)& 8a^4-7a^{3}b-6a^2{b}^2-4a{b}^3+7b^4& 5& \text{Polynomial}\\ e)& -p^4{q}^3& 1& \text{Monomial}\end{array}$

Step 2. Determine the number of terms

$\begin{array}{cccc}& \text{Polynomial}& \begin{array}{l}\text{Degreeof}\\ \text{terms}\end{array}& \text{Degree}\\ a)& 64k^3-8& 3,0& \text{3}\\ b)& 9m^3+4m^2-2& 3,2,0& \text{3}\\ c)& \frac{5}{6}& 0& \text{0}\\ d)& 8a^4-7a^{3}b-6a^2{b}^2-4a{b}^3+7b^4& 4,4,4,4,4& \text{4}\\ e)& -p^4{q}^3& 7& \text{7}\end{array}$