Factor Theorem Calculator

To apply the Factor Theorem, evaluate the polynomial f(x) at a value a. If f(a)=0, then x – ax−a is a factor of f(x). This theorem is useful in polynomial division and finding roots of polynomials.

The Factor Theorem Calculator is primarily developed to calculate if a given value is a factor of a polynomial. This theorem states that for any polynomial , if $f(a) = 0$ , then is a factor of $f (x)$ .

Thus, it simplifies the process of factoring and finding real zeros of polynomials, especially in algebra and calculus. In fact, by using this calculator, students and professionals can quickly verify factors of polynomials, making complex algebraic computations much easier.

Formula:

Contents

1 Formula:
2 Solved Calculations
3 What is a Factor Theorem Calculator?
4 Final Words:

 $f(x) = (x - a) \cdot q(x) +$

Variable	Description
$f(x)$	Polynomial function
$x$	Variable of the polynomial
$a$	Specific value for factor evaluation
$q(x)$	Quotient when dividing $f(x)$ by $x – a$
$r$	Remainder, which should be 0 if $x – a$ is a factor

Solved Calculations

Example 1:
For the polynomial $f(x) = x^2 – 5x + 6$ , determine if $x – 2$ is a factor.

Step	Calculation
1.	Substitute $a = 2$ into $f(x)$ : $f (2) = 2^{2} - 5 \cdot 2 + 6$
2.	$f (2) = 4 - 10 + 6 = 0$
3.	Since $f(2) = 0$ , $x – 2$ is a factor

Answer: $x – 2$ is a factor

Example 2:
For the polynomial $f(x) = x^3 – 7x + 6$ , check if $x – 1$ is a factor.

Step	Calculation
1.	Substitute $a = 1$ into $f(x)$ : $f(1) = 1^3 – 7 \cdot 1 + 6$
2.	$f(1) = 1 – 7 + 6 = 0$
3.	Since $f (1) = 0$ , $x – 1$ is a factor

Answer: $x – 1$ is a factor

What is a Factor Theorem Calculator?

The Factor Theorem Calculator is a tool designed to help you find out if a given value is a factor of a polynomial.

Simply, by entering a polynomial and a potential factor, this calculator checks if the polynomial has a zero at that value, indicating it’s a factor. To talk about its applications, this tool is particularly useful in algebra for simplifying polynomial expressions and finding all real zeros.

The calculator leverages both the Factor Theorem and the Remainder Theorem, allowing users to input values and evaluate them through synthetic division or other methods.

Final Words:

In brief, the Factor Theorem Calculator streamlines the process of factoring polynomials, making it an essential tool for solving algebraic equations and understanding polynomial behavior.