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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 504 (page 564)

(a) Is it a monomial, binomial, or trinomial?
(b) What is its degree?
$(n - 8) (n^{2} - 4 n + 11)$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information

The given polynomial is $(n - 8) (n^{2} - 4 n + 11)$ .

02

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

Simplify the given expression as follows:

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

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

03

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.

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