Factor Polynomials Calculator

This calculator helps users factor polynomials by determining the roots and presenting the polynomial in its factored form based on the provided coefficients and degree (quadratic or cubic).

Use Our Factor Polynomials Calculator

Using the Factor Polynomials Calculator

The Factor Polynomials Calculator is a convenient tool for calculating the roots and factoring quadratic and cubic polynomials. This step-by-step guide will help you to utilize the calculator efficiently.

Step 1: Selecting the Polynomial Degree

To start, select the degree of the polynomial you want to factor:

  • Choose Quadratic (ax² + bx + c) if your polynomial is of degree 2.
  • Choose Cubic (ax³ + bx² + cx + d) if your polynomial is of degree 3.

This selection is crucial as it determines the number of coefficients you’ll need to input subsequently.

Step 2: Entering Coefficients

Input the necessary coefficients for your chosen polynomial degree:

  • For a Quadratic polynomial, enter values for:
    • Coefficient a: This is the coefficient of the x² term. Enter a value between -1000 and 1000.
    • Coefficient b: This is the coefficient of the x term. Enter a value between -1000 and 1000.
    • Coefficient c: This is the constant term. Enter a value between -1000 and 1000.
  • For a Cubic polynomial, in addition to the above, enter:
    • Coefficient d: This is an optional coefficient for the constant term in cubic polynomials. Enter a value between -1000 and 1000.

Ensure all coefficients are entered correctly to obtain accurate results.

Step 3: Viewing the Results

Once you’ve entered all the required coefficients, the calculator will provide the following results:

  • Discriminant: This value helps in determining the nature of the roots for the polynomial.
  • Roots: The calculator will provide you with one or more roots (known as solutions) based on the polynomial degree.
    • The Quadratic option will display Root 1 and Root 2.
    • The Cubic option will also display Root 3, specific to cubic polynomials.
  • Factored Form: This represents the polynomial in its factored state as a product of its factors, providing insight into its roots.

Step 4: Interpret the Output

Understand the results and use the factored form, along with the roots, to gain insights into the behavior and roots of the polynomial. This information can be useful in various mathematical analyses and applications.

By following these steps, you can effectively use the Factor Polynomials Calculator to analyze and factor quadratic and cubic polynomials.