Chapter 6: Q. 8 (page 696)

In the following exercises, determine the degree of each polynomial.
$ⓐ 62 y^{2} ⓑ 15 ⓒ 6 x^{2} - 3 x y + 4 x - 2 y + y^{2} ⓓ 10 - 9 x ⓔ m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1$

Short Answer

Expert verified

$ⓐ 62 y^{2} degree is 2 . ⓑ 15 degree is 0 . ⓒ 6 x^{2} - 3 x y + 4 x - 2 y + y^{2} degree is 2 . ⓓ 10 - 9 x degree is 1 . ⓔ m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1 degree is 4 .$

Step by step solution

Step 1. Give Information

In the given exercises, we have to determine the degree of each polynomial.

$ⓐ 62 y^{2} ⓑ 15 ⓒ 6 x^{2} - 3 x y + 4 x - 2 y + y^{2} ⓓ 10 - 9 x ⓔ m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1$

Part (a) Step 1. The polynomial is 62y2

The exponent of y is two. So the degree is 2.

Part (b) Step 1. The polynomial is 15

The degree of a constant is $0$ . So the degree is $0$ .

Part (c) Step 1. The polynomial is 6x2−3xy+4x−2y+y2

The highest degree of all the terms is 2. So the degree is 2.

Part (d) Step 1. The polynomial is 10−9x

The highest degree of all the terms is 1. So the degree is 1.

Part (e) Step 1. The polynomial is m4+4m3+6m2+4m+1

The highest degree of all the terms is 4. So the degree is 4.

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 the degree of each polynomial.
$ⓐ 62 y^{2} ⓑ 15 ⓒ 6 x^{2} - 3 x y + 4 x - 2 y + y^{2} ⓓ 10 - 9 x ⓔ m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1$

Short Answer

Step by step solution

Step 1. Give Information

Part (a) Step 1. The polynomial is 62y2

Part (b) Step 1. The polynomial is 15

Part (c) Step 1. The polynomial is 6x2−3xy+4x−2y+y2

Part (d) Step 1. The polynomial is 10−9x

Part (e) Step 1. The polynomial is m4+4m3+6m2+4m+1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Discrete Mathematics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, determine the degree of each polynomial.ⓐ62y2ⓑ15ⓒ6x2−3xy+4x−2y+y2ⓓ10−9xⓔm4+4m3+6m2+4m+1

Short Answer

Step by step solution

Step 1. Give Information

Part (a) Step 1. The polynomial is 62y2

Part (b) Step 1. The polynomial is 15

Part (c) Step 1. The polynomial is 6x2−3xy+4x−2y+y2

Part (d) Step 1. The polynomial is 10−9x

Part (e) Step 1. The polynomial is m4+4m3+6m2+4m+1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Discrete Mathematics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, determine the degree of each polynomial.
$ⓐ 62 y^{2} ⓑ 15 ⓒ 6 x^{2} - 3 x y + 4 x - 2 y + y^{2} ⓓ 10 - 9 x ⓔ m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1$