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Questions and Answers
What is an algebraic expression?
What is an algebraic expression?
- A mathematical phrase that cannot be determined true or false
- A numerical value
- A mathematical expression containing one or more variables (correct)
- A letter or symbol used to represent an unknown
What is the definition of a coefficient?
What is the definition of a coefficient?
- The constant preceding the variables in a product (correct)
- An unknown quantity
- A mathematical phrase
- A constant value
What is a constant?
What is a constant?
A numerical value
What is an expression?
What is an expression?
What is a variable?
What is a variable?
If x is 5, then 6x = _____.
If x is 5, then 6x = _____.
What is the expression for the sum of n and five?
What is the expression for the sum of n and five?
What is the expression for five subtracted from n?
What is the expression for five subtracted from n?
What is the expression for eight added to x?
What is the expression for eight added to x?
What is the expression for eight subtracted from x?
What is the expression for eight subtracted from x?
What is the expression for eight minus x?
What is the expression for eight minus x?
What is the expression for five minus n?
What is the expression for five minus n?
What is the expression for x added to the sum of five and seven?
What is the expression for x added to the sum of five and seven?
What is the expression for the sum of eight and two, subtracted from x?
What is the expression for the sum of eight and two, subtracted from x?
What is the expression for the difference of eight and two, added to x?
What is the expression for the difference of eight and two, added to x?
What is the expression for the sum of x and itself?
What is the expression for the sum of x and itself?
Which expression does not represent 'the sum of n and 6'?
Which expression does not represent 'the sum of n and 6'?
Which of the following expressions represents 'the difference of 8 and n'?
Which of the following expressions represents 'the difference of 8 and n'?
Which of the following expressions does not represent 'four more than one-third x'?
Which of the following expressions does not represent 'four more than one-third x'?
Which of the following expressions represents 'twelve diminished by six times a number'?
Which of the following expressions represents 'twelve diminished by six times a number'?
Which of the following expressions represents 'three times the difference between t and y'?
Which of the following expressions represents 'three times the difference between t and y'?
Which of the following expressions represents 'the quotient of nine times a number and seven'?
Which of the following expressions represents 'the quotient of nine times a number and seven'?
Which of the following expressions represents 'the sum of n and the sum of 8 and 6'?
Which of the following expressions represents 'the sum of n and the sum of 8 and 6'?
The coefficient of 6x is _____.
The coefficient of 6x is _____.
The coefficient of 8 + 2N is _____.
The coefficient of 8 + 2N is _____.
The coefficient of 9(14)P is _____.
The coefficient of 9(14)P is _____.
The coefficient of 2(3)(6)Q is _____.
The coefficient of 2(3)(6)Q is _____.
Look at each expression. Is it equivalent to 'the quotient of 10 plus x and y minus 3'?
Look at each expression. Is it equivalent to 'the quotient of 10 plus x and y minus 3'?
For 3x^2 - 4x + 1, match the following:
For 3x^2 - 4x + 1, match the following:
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Study Notes
Key Definitions
- Algebraic Expression: A mathematical expression that includes one or more variables.
- Coefficient: The constant factor that multiplies a variable in an expression.
- Constant: A fixed numerical value not affected by variables.
- Expression: A mathematical phrase that represents a value but cannot be classified as true or false.
- Variable: A symbol or letter that stands for an unknown number.
Mathematical Operations with Variables
- Example when x = 5: Substituting gives ( 6x = 30 ).
- The sum of ( n ) and five: Written as ( n + 5 ).
- Five subtracted from ( n ): Written as ( n - 5 ).
- Eight added to ( x ): Expressed as ( x + 8 ).
- Eight subtracted from ( x ): Expressed as ( x - 8 ).
- Eight minus ( x ): Presented as ( 8 - x ).
- Five minus ( n ): Expressed as ( 5 - n ).
- ( x ) added to the sum of five and seven: Written as ( x + (5 + 7) ).
- The sum of eight and two, subtracted from ( x ): Written as ( x - (8 + 2) ).
- The difference of eight and two, added to ( x ): Expressed as ( x + (8 - 2) ).
- The sum of ( x ) and itself: Written as ( x + x ).
Expression Evaluation and Identification
- Incorrect representation of "the sum of ( n ) and 6": ( 6n ) (not ( 6 + n ) or ( n + 6 )).
- Correct representation of "the difference of 8 and ( n )": ( 8 - n ) (not ( n - 8 ) or (-8n)).
- Incorrect option for "four more than one-third ( x )": ( 1/4x + 3 ).
- Correct representation of "twelve diminished by six times a number": ( 12 - 6n ).
Coefficient Analysis
- Coefficient of ( 6x ): 6.
- Coefficient of ( 8 + 2N ): 16 (from multiplying 8 and 2).
- Coefficient of ( 9(14)P ): 126 (product of 9 and 14).
- Coefficient of ( 2(3)(6)Q ): 36 (product of 2, 3, and 6).
Expression Equivalence
- For expression ( \frac{10 + x}{y - 3} ):
- ( \frac{10+x}{y} ): No
- ( \frac{10+x}{y-3} ): Yes
- ( 10 + \frac{x}{y} - 3 ): No
- ( \frac{10 + x - 3}{y} ): No
Properties of Algebraic Expressions
- For the expression ( 3x^2 - 4x + 1 ):
- Variable: ( x ).
- Coefficient: 3 (of the term ( 3x^2 )).
- Constant: 1 (the standalone integer).
- Algebraic Expression: ( 3x^2 - 4x + 1 ).
- Degree: 2 (highest power of variable ( x )).
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