Constant Term

Definition

The constant term in an algebraic expression or equation is the numerical value that does not have a variable associated with it. It is the term that remains constant regardless of the values assigned to the variables in the expression.

5 Must Know Facts For Your Next Test

1. The constant term is essential in solving linear equations, as it represents the value that must be isolated on one side of the equation.
2. When solving equations with variables and constants on both sides, the constant terms on each side must be combined to find the solution.
3. Equations with fraction or decimal coefficients can still have constant terms, which must be properly handled during the solving process.
4. Constant terms are added or subtracted when performing operations on polynomials, just like the variable terms.
5. The constant term in a polynomial expression does not change when the variable values change, unlike the variable terms.

Review Questions

• Explain the role of the constant term in solving linear equations using the addition and subtraction properties of equality.
  • The constant term in a linear equation represents the fixed value that must be isolated on one side of the equation in order to solve for the variable. When using the addition and subtraction properties of equality to solve the equation, the constant terms on each side of the equation are combined and simplified to find the solution. For example, in the equation $2x + 5 = 11$, the constant term is 5, and it must be subtracted from both sides to isolate the variable term $2x$ and find the value of $x$.
• Describe how the constant term is handled when solving equations with variables and constants on both sides.
  • When solving equations with variables and constants on both sides, the constant terms must be combined and simplified on each side of the equation. This allows the variable terms to be isolated and solved for. For instance, in the equation $3x + 4 = 2x + 7$, the constant terms are 4 and 7. These must be combined by subtracting 4 from 7 to get a constant term of 3 on the right side of the equation. This step is crucial in order to then isolate the variable $x$ and find its value.
• Analyze the role of the constant term when adding and subtracting polynomials, and explain how it impacts the overall expression.
  • When adding or subtracting polynomials, the constant terms are treated the same as the variable terms. The constant terms are combined by adding or subtracting them directly. This means that the constant term in the final polynomial expression will reflect the sum or difference of the constant terms from the original polynomials. The constant term is an essential component of the overall polynomial, as it represents the fixed, non-variable portion of the expression. Neglecting or mishandling the constant term can lead to incorrect results when performing polynomial operations.

Related terms

Variable: A symbol, usually a letter, that represents an unknown or changeable quantity in an algebraic expression.

Coefficient: The numerical factor multiplied by a variable in an algebraic expression.

Polynomial: An algebraic expression consisting of variables and coefficients, where the variables are only raised to non-negative integer powers.