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Module 7: Algebra

Introduction and Terminology

As you may have already seen, mathematics is a mixture of operations, signs, numbers, and symbols. The numbers are concrete values, constants that can be manipulated to form new values. Symbols (or variables) typically come in the form of letters. While we can still apply operations, they do not possess any concrete value unless we assign one or solve for them in context. This is known as algebra.

Below is a list of algebraic vocabulary you should familiarize yourself with.

We'll use the following expression throughout the table as a common reference point: x 2 + 2 x − 6 x + 3 y + 4 {"version":"1.1","math":"x^2 + 2x - 6x + 3y + 4"}

Algebraic Term Definition Example
Algebraic Expression
  • Mathematical equation that are composed of various terms of known and unknown quantities.
 x 2 + 2 x − 6 x + 3 y + 4 {"version":"1.1","math":"x^2 + 2x - 6x + 3y + 4"}
Term
  • Value of an expression that can be manipulated by addition, subtraction. Can include signs, variables, constants, coefficients.
  • Like: terms that contain the same variables and order (can be combined).
  • Unlike: terms that do not contain the same variables and/or order (can’t be combined).

2 x , − 6 x , 3 y , 4 {"version":"1.1","math":"2x,\; -6x,\; 3y,\; 4 "}

Notice that the sign is also associated with the term.

2 x , − 6 x {"version":"1.1","math":"2x,\; -6x "}

 

3 y , 4 , 2 x , x 2 {"version":"1.1","math":"3y,\; 4,\; 2x,\; x^2 "}
Variable
  • Letter or symbol used to represent some number.
  • Factor of its respective term.

x , y {"version":"1.1","math":"x,y "}

y {"version":"1.1","math":"y"} is a factor of 3 y {"version":"1.1","math":"3y"}
Contant
  • Term that includes only a number and no variable.
  • Factor of its respective term.

4 {"version":"1.1","math":"4"}
Coefficient
  • Number in a term associated with the variable/s.
  • Factor of its respective term.

In 2 x {"version":"1.1","math":"2x"}, 2 {"version":"1.1","math":"2"} is the coefficient.

2 {"version":"1.1","math":"2"} is a factor of 2 x {"version":"1.1","math":"2x"}, 2 {"version":"1.1","math":"2"}.

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