Constant Term

Definition

The constant term, also known as the constant, is a numerical value in an equation or expression that does not depend on any variable. It is the term that remains fixed and unchanging, regardless of the values assigned to the variables.

5 Must Know Facts For Your Next Test

1. The constant term is a crucial component in solving equations, as it represents the value that the expression must equal when all variables are eliminated.
2. In the context of solving systems of equations, the constant terms are used to determine the point of intersection between the equations.
3. When adding or subtracting polynomials, the constant terms are combined to form a single constant term in the resulting expression.
4. The constant term plays a significant role in factoring trinomials, as it is one of the values used to determine the factors of the expression.
5. In the process of solving quadratic equations, the constant term is used in both the square root property and the method of completing the square.

Review Questions

• Explain the role of the constant term in solving equations using the Division and Multiplication Properties of Equality.
  • When solving equations using the Division and Multiplication Properties of Equality, the constant term is essential. The constant term represents the value that the expression must equal after all variables have been isolated and eliminated. By performing inverse operations to isolate the variable, the constant term is used to determine the final solution to the equation.
• Describe how the constant term is used in the process of solving systems of equations by graphing.
  • In the context of solving systems of equations by graphing, the constant terms are crucial in determining the point of intersection between the equations. The constant terms are used to plot the y-intercept of each line, and the point where the lines intersect represents the solution to the system, which satisfies both equations simultaneously.
• Analyze the importance of the constant term when adding and subtracting polynomials.
  • When adding or subtracting polynomials, the constant terms are combined to form a single constant term in the resulting expression. This is because the constant term is the term that does not depend on any variable, and it can be treated as a single value that is added or subtracted independently from the variable terms. Understanding the role of the constant term in these polynomial operations is essential for simplifying and manipulating polynomial expressions.

Related terms

Variable:

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

Coefficient:

A coefficient is a numerical value that multiplies a variable in an equation or expression.

Linear Equation:

A linear equation is an equation in which the highest exponent of the variable is 1, and the equation can be written in the form $ax + b = 0$, where $a$ and $b$ are constants.