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Solving by Factoring Calculator

Roots = Solve(factored = 0)

\[ \text{If } (x - a)(x - b) = 0, \text{ then } x = a \text{ or } x = b \]

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1. What is Solving by Factoring?

Solving by factoring is a method to find the roots (solutions) of a polynomial equation by expressing it as a product of its factors and setting each factor equal to zero.

2. How Does the Calculator Work?

The calculator uses the Zero Product Property:

\[ \text{If } (x - a)(x - b) = 0, \text{ then } x = a \text{ or } x = b \]

Steps:

  1. Enter a factored polynomial equation set to zero
  2. The calculator identifies each factor
  3. Sets each factor equal to zero
  4. Solves for the variable to find all roots

3. Importance of Factoring

Details: Factoring is a fundamental algebra skill used to solve quadratic equations, find x-intercepts of parabolas, and analyze polynomial functions.

4. Using the Calculator

Tips: Enter equations in factored form set to zero (e.g., "(x-2)(x+3)=0"). For best results, use simple integer factors.

5. Frequently Asked Questions (FAQ)

Q1: What types of equations can this calculator solve?
A: It solves polynomial equations that are already in factored form and set equal to zero.

Q2: Can it factor equations for me?
A: No, this calculator only solves equations that are already factored.

Q3: What if my equation isn't set to zero?
A: You must rewrite the equation in standard form (set to zero) before factoring.

Q4: How many roots can a polynomial have?
A: A polynomial of degree n can have up to n real roots.

Q5: What about complex roots?
A: This calculator currently only displays real roots.

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