Factor to Polynomial Calculator

🛡️ Reviewed by David Chen, CFA — Professional Mathematician & Financial Analyst

Effortlessly convert factored algebraic expressions into their standard polynomial form. This factor to polynomial calculator uses advanced expansion algorithms to provide accurate coefficients and detailed step-by-step solutions for your mathematical equations.

Factor to Polynomial Calculator

Enter the roots $r_1, r_2…$ to solve $(x – r_1)(x – r_2)…$

Factor to Polynomial Formula

The standard conversion from factored form to polynomial form is defined by the product of linear factors:

$P(x) = a(x – r_1)(x – r_2)(x – r_3)…(x – r_n)$

Source: WolframAlpha Polynomials, Khan Academy Algebra

Variables:

• $r_n$ (Roots): The specific values of $x$ where the polynomial equals zero.
• $a$ (Leading Coefficient): A constant factor that scales the entire polynomial.
• $x$: The independent variable of the function.

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What is a Factor to Polynomial Calculator?

A Factor to Polynomial Calculator is a mathematical tool that expands algebraic expressions from their factored form into standard polynomial form ($ax^n + bx^{n-1} + … + k$). This process is essential in calculus, physics, and engineering when analyzing the behavior of functions and finding intersections.

By identifying the “zeros” or “roots” of a function, users can reconstruct the original equation. This calculator automates the tedious distributive multiplication (FOIL method) required for higher-degree polynomials.

How to Calculate (Example)

1. Identify your roots: e.g., $x = 1$ and $x = -2$.
2. Write the factors: $(x – 1)$ and $(x – (-2))$ which is $(x + 2)$.
3. Multiply the first two factors: $(x – 1)(x + 2) = x^2 + 2x – x – 2$.
4. Simplify the expression: $x^2 + x – 2$.
5. Multiply by the leading coefficient $a$ if applicable.

Frequently Asked Questions (FAQ)

What does it mean to “expand” a polynomial? Expansion is the process of multiplying factors together to remove parentheses and express the equation as a sum of terms.

Can this calculator handle complex roots? This version focuses on real numbers. For complex roots, ensure you input them in the proper numerical format.

Why is the leading coefficient important? The leading coefficient determines the “stretch” or “compression” of the graph and its end behavior, even if the roots remain the same.

How many roots can I enter? You can enter any number of roots; however, the degree of the polynomial increases with each root added.