Factor Trinomials Calculator

The Factor Trinomials Calculator helps users factor quadratic trinomials by providing the discriminant, roots, and corresponding binomial factors based on coefficients provided for x², x, and the constant term.

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Using the Factor Trinomials Calculator

This guide will walk you through the process of utilizing the Factor Trinomials Calculator to find the roots and factors of a quadratic trinomial of the form ax² + bx + c.

Inputting Coefficients

  1. Identify the coefficients: The trinomial you want to factor will be of the form ax² + bx + c. Identify the values for a, b, and c in your equation.
  2. Enter these coefficients into the calculator:
    • For the coefficient of x² (a), enter the number in the input field labeled “Coefficient of x² (a)”. Ensure the value is between -100 and 100.
    • For the coefficient of x (b), fill in the number in the input field marked “Coefficient of x (b)”. Make sure it is within the range of -100 to 100.
    • Finally, for the constant term (c), input the number in the field labeled “Constant term (c)”. The acceptable range is -100 to 100.

All input fields are required, and the values must be integers between the specified limits.

Understanding the Result Fields

  1. Discriminant: The calculator will compute the discriminant using the formula b² – 4ac. This value is crucial in determining the nature of the roots (real or complex) of the equation.
  2. Roots: Based on the discriminant, the calculator will determine the roots of the equation:
    • First Root (root1): Calculated using the formula (-b + √(b² - 4ac)) / (2a), this is one of the solutions to the quadratic equation.
    • Second Root (root2): Found using the formula (-b - √(b² - 4ac)) / (2a), this represents the other solution.
  3. Factors: These roots will then be used to express the trinomial in its factored form:
    • First Factor (factor1): Shown as (ax + (-root1 * a)), this represents one part of the factored expression.
    • Second Factor (factor2): Displayed as (ax + (-root2 * a)), completing the other component of the factoring.

The results will be presented with appropriate numeric formatting, ensuring that all calculated values display up to two decimal places for precision.