Question

(a) Is it a monomial, binomial, or trinomial?

(b) What is its degree?

$\left(n-8\right)\left(n^2-4n+11\right)$

Short answer

The given polynomial is not a monomial, binomial, or trinomial and its degree is 3.

Step-by-step solution

Step 1. Given Information

The given polynomial is$\left(n-8\right)\left(n^2-4n+11\right)$.

Part (a) Step 1. Count the Terms in Simplified Polynomial

• Simplify the given expression as follows:

$\begin{array}{rcl}\left(n-8\right)\left(n^2-4n+11\right)& =& n^3-4n^2+11n-8n^2+32n-88\\ & =& n^3-12n^2+43n-88\end{array}$

• As the polynomial has four terms, it is not a monomial, binomial, or trinomial.

Part (b) Step 1. Find the Highest Power 

• The term with highest power of the variable in the simplified polynomial is $n^3$
• The exponent of this term is 3.
• So the degree of the trinomial is 3.