Factoring Trinomials Calculator

The Factoring Trinomials Calculator helps users factor quadratic trinomials by calculating discriminants and factors, and determining if the trinomial has rational roots.

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How to Use the Factoring Trinomials Calculator

This guide will walk you through the process of using the Factoring Trinomials Calculator to find the factors of a trinomial of the form ax² + bx + c. Follow the steps below to input your coefficients and understand the results.

Step 1: Input the Coefficients

  • Enter the Coefficient of x² (a): In the text field labeled “Coefficient of x² (a)”, input the value for ‘a’. Ensure that this number is between -100 and 100, as these are the acceptable range limits. The field accepts whole numbers (step size of 1).
  • Enter the Coefficient of x (b): Enter the value for ‘b’ in the text field labeled “Coefficient of x (b)”. This number should also be within the range of -100 to 100 and must be a whole number.
  • Enter the Constant Term (c): In the field labeled “Constant Term (c)”, provide your value for ‘c’. It should be a whole number within the prescribed range, from -100 to 100.

Step 2: Understand the Result Fields

  • Discriminant: Upon entering all the coefficients, the calculator will compute the discriminant using the formula: b² – 4ac. This value is crucial in determining the type and number of solutions (factors) the trinomial has.
  • First Factor and Second Factor: If the discriminant is non-negative, the calculator will show you the first and second factors, calculated as -b ± √(b² - 4ac) / 2a. These calculations are rounded to two decimal places.
  • Has Rational Factors: The calculator will indicate whether the trinomial can be factored into rational numbers. If the discriminant is greater than or equal to zero, it will display “Yes”, otherwise “No”.
  • Factored Form: Based on the discriminant and the calculated factors, the calculator will output the factored form of the trinomial. If factoring is possible in real numbers, it will show the expression as (x + factor1)(x + factor2). If not, it will state that the trinomial is “Not factorable in real numbers”.

By following these steps, you can seamlessly use the Factoring Trinomials Calculator to determine the factors of any trinomial expression you are working with.