Constant

Definition

A constant is a quantity in an algebraic expression or equation that has a fixed, unchanging value. It is a value that does not vary or change throughout the given context or problem.

5 Must Know Facts For Your Next Test

1. Constants are important in algebra because they provide the fixed values that variables can be compared to or operate on.
2. Evaluating algebraic expressions often involves substituting constant values for the variables.
3. When solving equations, constants on one side of the equation can be used to isolate the variable on the other side.
4. The Distributive Property allows constants to be factored out of polynomial expressions.
5. Formulas in mathematics and science often contain constants that represent universal or defined values.

Review Questions

• Explain how constants are used in the context of evaluating, simplifying, and translating algebraic expressions.
  • When evaluating an algebraic expression, constants are the fixed values that are substituted in place of the variables. This allows the expression to be simplified down to a single numerical value. Similarly, when translating verbal statements into algebraic expressions, constants represent the known or given quantities that are not changing. Simplifying an expression often involves combining like terms, where the constants are added or multiplied together separately from the variables.
• Describe the role of constants in solving equations using the Division and Multiplication Properties of Equality.
  • When solving equations, the goal is to isolate the variable by performing inverse operations. The Division and Multiplication Properties of Equality allow you to divide or multiply both sides of an equation by the same constant in order to eliminate the constant term and leave only the variable. This is an essential step in solving linear equations with variables and constants on both sides, as well as formulas that need to be solved for a specific variable.
• Analyze how the Distributive Property allows constants to be factored out of polynomial expressions.
  • The Distributive Property states that a constant multiplied by a sum is equal to the sum of the products of the constant with each addend. This means that any constant factor in a polynomial expression can be factored out, leaving just the variable terms behind. This is a useful simplification technique that can reveal the structure of more complex polynomial expressions and make them easier to work with, especially when multiplying or dividing polynomials.

Related terms

Variable: A variable is a symbol, usually a letter, that represents an unknown or changing quantity in an algebraic expression or equation.

Coefficient: A coefficient is a numerical factor that multiplies a variable in an algebraic expression.

Equation: An equation is a mathematical statement that expresses the equality of two expressions.