Chapter 5: Q. 1 (page 497)

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.
$\begin{array}{l} (a) 47 x^{5} - 17 x^{2} y^{3} + y^{2} \\ (b) 5 c^{3} + 11 c^{2} - c - 8 \\ (c) \frac{5}{9} a b + \frac{1}{3} b \\ (d) 4 \\ (e) 4 p q + 17 \end{array}$

Short Answer

Expert verified

The type of the polynomials is $\begin{matrix} Polynomial & Type & Degree \\ a) & 47 x^{5} - 17 x^{2} y^{3} + y^{2} & Trinomial & 5 \\ b) & 5 c^{3} + 11 c^{2} - c - 8 & Polynomial & 3 \\ c) & \frac{5}{9} a b + \frac{1}{3} b & Binomial & 2 \\ d) & 4 & Monomial & 0 \\ e) & 4 p q + 17 & Binomial & 2 \end{matrix}$ $\begin{matrix} Polynomial & Type & Degree \\ a) & 47 x^{5} - 17 x^{2} y^{3} + y^{2} & Trinomial & 5 \\ b) & 5 c^{3} + 11 c^{2} - c - 8 & Polynomial & 3 \\ c) & \frac{5}{9} a b + \frac{1}{3} b & Binomial & 2 \\ d) & 4 & Monomial & 0 \\ e) & 4 p q + 17 & Binomial & 2 \end{matrix}$

Step by step solution

Step 1. Given information

The polynomial expressions given are

$\begin{array}{l} (a) 47 x^{5} - 17 x^{2} y^{3} + y^{2} \\ (b) 5 c^{3} + 11 c^{2} - c - 8 \\ (c) \frac{5}{9} a b + \frac{1}{3} b \\ (d) 4 \\ (e) 4 p q + 17 \end{array}$

Step 2. Determine the type of the polynomial

$\begin{matrix} Polynomial & Numberofterms & Type \\ a) & 47 x^{5} - 17 x^{2} y^{3} + y^{2} & 3 & Trinomial \\ b) & 5 c^{3} + 11 c^{2} - c - 8 & 4 & Polynomial \\ c) & \frac{5}{9} a b + \frac{1}{3} b & 2 & Binomial \\ d) & 4 & 1 & Monomial \\ e) & 4 p q + 17 & 2 & Binomial \end{matrix}$

Step 3. Determine the degree of the polynomial

$\begin{matrix} Polynomial & Degreeofterms & Degree \\ a) & 47 x^{5} - 17 x^{2} y^{3} + y^{2} & 5, 5, 2 & 5 \\ b) & 5 c^{3} + 11 c^{2} - c - 8 & 3, 2, 1, 0 & 3 \\ c) & \frac{5}{9} a b + \frac{1}{3} b & 2, 1 & 2 \\ d) & 4 & 0 & 0 \\ e) & 4 p q + 17 & 2 & 2 \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.
$\begin{array}{l} (a) 47 x^{5} - 17 x^{2} y^{3} + y^{2} \\ (b) 5 c^{3} + 11 c^{2} - c - 8 \\ (c) \frac{5}{9} a b + \frac{1}{3} b \\ (d) 4 \\ (e) 4 p q + 17 \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the type of the polynomial

Step 3. Determine the degree of the polynomial

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.(a)47x5−17x2y3+y2(b)5c3+11c2−c−8(c)59ab+13b(d)4(e)4pq+17

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the type of the polynomial

Step 3. Determine the degree of the polynomial

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.
$\begin{array}{l} (a) 47 x^{5} - 17 x^{2} y^{3} + y^{2} \\ (b) 5 c^{3} + 11 c^{2} - c - 8 \\ (c) \frac{5}{9} a b + \frac{1}{3} b \\ (d) 4 \\ (e) 4 p q + 17 \end{array}$