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.

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