Polynomial Factoring Calculator

Using the Polynomial Factoring Calculator

This guide provides step-by-step instructions on how to use the Polynomial Factoring Calculator to find the roots and the factored form of quadratic and cubic polynomials.

Step 1: Selecting the Polynomial Degree

Begin by selecting the degree of the polynomial you want to factor from the dropdown menu labeled Polynomial Degree. You can choose between:

• Quadratic (ax² + bx + c): Select this option if you are working with second-degree polynomials.
• Cubic (ax³ + bx² + cx + d): Select this option for third-degree polynomials.

Step 2: Entering Coefficients

After selecting the polynomial degree, enter the coefficients for your polynomial in the input fields provided:

• Coefficient a: Enter the coefficient of the highest degree term. This field is required and accepts values between -1000 and 1000, with a precision of two decimal places.
• Coefficient b: Enter the coefficient of the next highest degree term (x term for quadratics). This field is also required and has the same range and precision as a.
• Coefficient c: Enter the constant term for quadratic polynomials. This field is required for quadratics and has the same range and precision as previous fields.
• Coefficient d (for cubic only): This field is for cubic polynomials to enter the constant term. It is optional and follows the same range and precision constraints as other coefficients.

Step 3: Calculate Results

Once you have entered all necessary coefficients, the calculator will automatically compute and display the results in the following fields:

• Discriminant: Shows the discriminant of the polynomial, calculated as (b² – 4ac). This value helps determine the nature of the roots.
• Root 1: Displays the first root of the polynomial, calculated using the quadratic formula for quadratics.
• Root 2: Displays the second root, similarly calculated using the quadratic formula.
• Factored Form: The polynomial expressed in its factored form using the calculated roots and coefficient a, e.g., a(x – root1)(x – root2).
• Root Type: Describes the nature of the roots based on the discriminant, indicating whether they are real and distinct, real and equal, or complex conjugates.

The results will be displayed with the appropriate decimal precision for better accuracy. Follow these instructions to successfully use the Polynomial Factoring Calculator to evaluate polynomial expressions.