Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 59PPS
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Question
![### Polynomial Addition Problem
Consider the following polynomial expression:
\[ (10x - 3 + 7x^2) + (x^2 - 2x + 17) \]
Which of the following options correctly represents the simplified form of the given polynomial expression?
**Options:**
A) \( 8x^2 + 9x + 10 \)
B) \( 11x^2 + 8 + 10x \)
C) \( 8x^2 + 8x + 15 \)
D) \( 10x^2 + 24x - 3 \)
### Steps to Solve:
1. **Arrange the Polynomial Terms by Degree:**
- Combine like terms (terms with the same power of \( x \)).
2. **Combine Like Terms:**
- For \( x^2 \) terms: \( 7x^2 + x^2 = 8x^2 \)
- For \( x \) terms: \( 10x - 2x = 8x \)
- For constant terms: \( -3 + 17 = 14 \)
3. **Simplify the Expression:**
- The simplified expression should be: \( 8x^2 + 8x + 14 \)
Based on the given options, the closest match to the simplified polynomial expression \( 8x^2 + 8x + 14 \) is not explicitly listed. Therefore, none of the provided options A, B, C, or D is correct.
**Note:** Ensure to review and verify mathematical operations when solving polynomial expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a800ae4-c2ca-495b-ad19-d1764829db07%2Fbf72602e-de00-4e22-98bc-315f8b2b99f8%2Fgboll6h.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Addition Problem
Consider the following polynomial expression:
\[ (10x - 3 + 7x^2) + (x^2 - 2x + 17) \]
Which of the following options correctly represents the simplified form of the given polynomial expression?
**Options:**
A) \( 8x^2 + 9x + 10 \)
B) \( 11x^2 + 8 + 10x \)
C) \( 8x^2 + 8x + 15 \)
D) \( 10x^2 + 24x - 3 \)
### Steps to Solve:
1. **Arrange the Polynomial Terms by Degree:**
- Combine like terms (terms with the same power of \( x \)).
2. **Combine Like Terms:**
- For \( x^2 \) terms: \( 7x^2 + x^2 = 8x^2 \)
- For \( x \) terms: \( 10x - 2x = 8x \)
- For constant terms: \( -3 + 17 = 14 \)
3. **Simplify the Expression:**
- The simplified expression should be: \( 8x^2 + 8x + 14 \)
Based on the given options, the closest match to the simplified polynomial expression \( 8x^2 + 8x + 14 \) is not explicitly listed. Therefore, none of the provided options A, B, C, or D is correct.
**Note:** Ensure to review and verify mathematical operations when solving polynomial expressions.
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