Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.5: Algebraic Expressions
Problem 90E: Building Envelope The building code in a certain town requires that a house be at least 10 ft from...
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![### Understanding Polynomials
**Question:**
How many terms does the polynomial \( x^2 + xy - y^2 \) have?
**Options:**
- [ ] 1 term
- [ ] 2 terms
- [ ] 3 terms
- [ ] 4 terms
### Explanation:
In this question, we are asked to identify the number of terms in a given polynomial.
A **polynomial** is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The given polynomial is:
\[ x^2 + xy - y^2 \]
**Steps to Identify Number of Terms:**
1. **Identify Each Term**: Break down the polynomial where each term is separated by a plus (+) or minus (−) sign.
- In \( x^2 \), \( xy \), and \( -y^2 \), these are separated by "+" and "−" signs.
2. **Count The Terms**: Count each distinct term.
- \( x^2 \) (first term)
- \( xy \) (second term)
- \( -y^2 \) (third term)
So, the polynomial \( x^2 + xy - y^2 \) has **3 terms**.
Correct answer:
- [ ] 1 term
- [ ] 2 terms
- [x] 3 terms
- [ ] 4 terms](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6036c7ed-53d1-4846-ab4e-c8ad76b07d27%2Ff78a2153-ff66-4211-bcbc-bdb669a34714%2Fwt7jd7b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Polynomials
**Question:**
How many terms does the polynomial \( x^2 + xy - y^2 \) have?
**Options:**
- [ ] 1 term
- [ ] 2 terms
- [ ] 3 terms
- [ ] 4 terms
### Explanation:
In this question, we are asked to identify the number of terms in a given polynomial.
A **polynomial** is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The given polynomial is:
\[ x^2 + xy - y^2 \]
**Steps to Identify Number of Terms:**
1. **Identify Each Term**: Break down the polynomial where each term is separated by a plus (+) or minus (−) sign.
- In \( x^2 \), \( xy \), and \( -y^2 \), these are separated by "+" and "−" signs.
2. **Count The Terms**: Count each distinct term.
- \( x^2 \) (first term)
- \( xy \) (second term)
- \( -y^2 \) (third term)
So, the polynomial \( x^2 + xy - y^2 \) has **3 terms**.
Correct answer:
- [ ] 1 term
- [ ] 2 terms
- [x] 3 terms
- [ ] 4 terms
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