Question

Parts of Algebraic Expressions Quick Check

Answer 1

Certainly! Here are some questions and concepts related to the parts of algebraic expressions. Use this as a quick check to evaluate your understanding:

### Quick Check on Parts of Algebraic Expressions

1. **Definitions**:
- Define the following terms:
- **Variable**
- **Coefficient**
- **Constant**
- **Term**
- **Expression**

2. **Identifying Parts**:
Given the algebraic expression \(3x^2 + 4y - 5\):
- Identify the coefficients.
- Identify the constants.
- Identify the terms.

3. **Combining Like Terms**:
Simplify the following expression by combining like terms:
\[ 7x + 3y - 2x + 4y + 9 \]

4. **Evaluating Expressions**:
Evaluate the expression \(2x + 3y - 7\) for \(x = 2\) and \(y = 5\).

5. **Creating Expressions**:
Write an algebraic expression for the following situation:
"Three times a number decreased by seven."

6. **Understanding Polynomials**:
Determine whether the following expression is a polynomial:
\[ 4x^3 - 2x^2 + x - 5 + \frac{1}{x} \]
Explain why or why not.

### Answers

1. **Definitions**:
- **Variable**: A letter that represents a number (e.g., \(x\), \(y\)).
- **Coefficient**: A numerical factor in front of a variable (e.g., in \(3x\), 3 is the coefficient).
- **Constant**: A fixed value that does not change (e.g., in the expression \(2x + 5\), 5 is a constant).
- **Term**: A single mathematical expression; it can be a number, variable, or like \(3xy\).
- **Expression**: A combination of numbers, variables, and operations that represents a value.

2. **Identifying Parts**:
- Coefficients: 3 (from \(3x^2\)), 4 (from \(4y\))
- Constant: -5
- Terms: \(3x^2\), \(4y\), \(-5\)

3. **Combining Like Terms**:
\[ (7x - 2x) + (3y + 4y) + 9 = 5x + 7y + 9 \]

4. **Evaluating Expressions**:
\[ 2(2) + 3(5) - 7 = 4 + 15 - 7 = 12 \]

5. **Creating Expressions**:
The expression is \(3x - 7\), where \(x\) is the number.

6. **Understanding Polynomials**:
No, the expression \(4x^3 - 2x^2 + x - 5 + \frac{1}{x}\) is not a polynomial because it contains \(\frac{1}{x}\), which is not a term with a non-negative integer exponent.

Feel free to ask if you need further explanations or have additional questions!