How many terms does the polynomial x² + xy - 2² have? Oooo 1 term 2 terms 3 terms 4 terms

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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
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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