Constant

Definition

A constant is a value or quantity that does not change within the context of a specific problem or equation. It is a fixed number or expression that remains the same throughout a mathematical operation or calculation.

5 Must Know Facts For Your Next Test

1. Constants are essential in solving linear equations, as they represent the known values in the equation.
2. When solving a formula for a specific variable, the constants in the formula remain unchanged throughout the process.
3. Polynomials can contain both variables and constants, which are added or subtracted based on their respective coefficients.
4. Rational expressions, which involve division, can also have constants in the numerator and denominator.
5. The presence of constants in an equation or expression helps to determine the relationships between the variables and known values.

Review Questions

• Explain the role of constants in solving linear equations using a general strategy.
  • When solving linear equations using a general strategy, the constants represent the known values that are isolated on one side of the equation. These constants are then used to determine the value of the variable by performing inverse operations to isolate the variable. The constants, along with the coefficients of the variable, guide the step-by-step process of solving the equation.
• Describe how constants are used when solving a formula for a specific variable.
  • When solving a formula for a specific variable, the constants in the formula remain unchanged throughout the process. The goal is to isolate the desired variable by performing algebraic operations, such as dividing or multiplying, to move the constants to one side of the equation. This allows the formula to be expressed in terms of the specific variable being solved for, with the constants serving as known values that are used in the final solution.
• Analyze the role of constants in the addition and subtraction of polynomials.
  • $$ In the context of adding and subtracting polynomials, the constants within the polynomial expressions are treated as fixed values that are combined based on their respective coefficients. The constants are added or subtracted directly, while the variables and their coefficients are also combined according to their like terms. The presence of constants in polynomial operations helps to maintain the overall structure and relationships within the expressions, allowing for the simplification and evaluation of the polynomial. $$

Related terms

Variable: A variable is a symbol, usually a letter, that represents an unknown or changing value within an equation or expression.

Coefficient: A coefficient is a numerical factor multiplied by a variable in an algebraic expression.

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