Factor Theorem Calculator

How to Use the Factor Theorem Calculator

Introduction

This guide will walk you through the steps necessary to use the Factor Theorem Calculator. This tool helps determine whether a given value is a factor of a polynomial by evaluating the polynomial at that value.

Step 1: Enter the Polynomial Coefficients

Start by entering the coefficients of your polynomial. You will need to provide:

• Coefficient of x³: This is the number that multiplies the cubic term in your polynomial. Enter this in the appropriate field.
• Coefficient of x²: Similarly, enter the coefficient of the quadratic term in your polynomial.
• Coefficient of x: Provide the coefficient of the linear term.
• Constant Term: Input the constant term without any variable multiplier.

Note: All these fields are required. Ensure to input accurate coefficients for a correct evaluation.

Step 2: Input a Value to Test

In the “Enter a value to test (potential factor)” field, input the number that you want to test as a potential factor of the polynomial.

This value will be substituted into the polynomial to calculate P(x).

Step 3: Evaluate the Result

Once all the required information is input, the calculator will compute the result. It evaluates P(x) by substituting the potential factor value into the polynomial expression, using the formula:

P(x) = (coefficient3 * x³) + (coefficient2 * x²) + (coefficient1 * x) + constantTerm

Step 4: Determine if it is a Factor

The calculator will also determine whether the value you tested is a factor by checking if the evaluated P(x) is zero (or very close to zero, considering a small threshold for computational precision).

The result field “Is it a factor?” will display “Yes, it is a factor” if the P(x) value is essentially zero, or “No, it is not a factor” if it is not.

Step 5: Verify Linear Factor

If the value you tested is indeed a factor, the corresponding linear factor in the form (x – the value) will be shown in the “Linear Factor (if applicable)” field, expressed with a precision of two decimal places for your convenience.

This indicates the divisor that divides the polynomial exactly without leaving a remainder.

By following these steps, you can effectively utilize the Factor Theorem Calculator to analyze and determine the factors of any given cubic polynomial.