College Algebra: Section 1.1b (Packet #2)
By the end of the section, you should be able to:
- Identify terms, coefficients, and factors in an algebraic expression.
- Simplify and/or Evaluate a mathematical expression (review from Alg. 2 Section 1.3).
- Identify the properties of real numbers (review from Alg. 2 Section 1.3).
- Use Venn diagrams to determine the value of basic set operations (Union and Intersection).
Definitions:
- Algebraic Expression: A mathematical phrase that contains one or more variables.
- Equation: a statement that two expressions are equal (=).
- Solution of an Equation: a value, or values of the variable that make the equation true.
- Literal Equation: an equation that uses at least two different letters as variables. With literal equations, the solution of the equation is “in terms of” the other variable(s).
- Simplify: combine all like terms and reduce the expression to the smallest number of terms possible.
- Evaluate: substitute a number in for each variable and simplify the expression using the order of operations.
- Constant: a value that does not change
- Variable: a symbol (usually a letter) that represents one or more numbers.
- Term: a number, variable, or the product of a number and one or more variables. Terms are separated by addition/subtraction.
- Constant Term: a term with no variables
- Like Terms: two or more terms with the same variables raised to the same power
- Coefficient: the numerical factor of a term.
- Factor: a number or variable that produces another number or expression through multiplication. Factors are separated by multiplication/division.
- Basic Set Operations: operations (similar to addition/subtraction) that are done to sets of numbers.
- Union: a set combining two sets of numbers including elements that are in the first set, the second set, or both sets.
- Intersection: a set combining two sets of numbers including only the elements that are in both the first set and the second set.
Examples of Identifying terms, coefficients, factors, and Evaluating Expressions
🎥 Example 1 🎥 Example 2
🎥 Example 1 🎥 Example 2
**For a more extensive review of simplifying/evaluating expressions, please see Algebra 2 Section 1.3
Basic Set Operations
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