Constant Term

Definition

The constant term is a numerical value in a polynomial or equation that does not depend on any variable. It is the term that remains unchanged regardless of the values assigned to the variables in the expression.

5 Must Know Facts For Your Next Test

1. In a polynomial expression, the constant term is the number or coefficient that is not multiplied by a variable.
2. The constant term plays a crucial role in the behavior and properties of quadratic equations, such as the location of the vertex and the shape of the parabola.
3. When solving a system of linear equations using Cramer's Rule, the constant terms are used to calculate the determinants that determine the unique solution.
4. The constant term in the equation of a parabola, $y = ax^2 + bx + c$, represents the $y$-intercept of the parabola.
5. The constant term can significantly impact the overall behavior and characteristics of an algebraic expression or equation.

Review Questions

• Explain the role of the constant term in a polynomial expression.
  • The constant term in a polynomial expression is the numerical value that does not depend on any variable. It is the term that remains unchanged regardless of the values assigned to the variables in the expression. The constant term plays a crucial role in the overall behavior and properties of the polynomial, such as the $y$-intercept and the end behavior of the graph.
• Describe how the constant term affects the solution of a quadratic equation.
  • In a quadratic equation of the form $ax^2 + bx + c = 0$, the constant term $c$ is a crucial factor that determines the nature and properties of the solutions. The constant term, along with the coefficients $a$ and $b$, determines the location of the vertex, the shape of the parabola, and the number and nature of the solutions (real or complex).
• Analyze the role of the constant term when solving a system of linear equations using Cramer's Rule.
  • When solving a system of linear equations using Cramer's Rule, the constant terms are used to calculate the determinants that determine the unique solution. The constant terms are essential in this process, as they are used to form the coefficient matrix and the matrices of the variables. The constant terms, along with the coefficients of the variables, are crucial in finding the values of the variables that satisfy the system of equations.

Related terms

Polynomial: A polynomial is an algebraic expression consisting of variables and coefficients, where the variables are raised to non-negative integer powers.

Quadratic Equation: A quadratic equation is a polynomial equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Cramer's Rule: Cramer's Rule is a method for solving systems of linear equations by using determinants to find the unique solution, if it exists.