# Factoring Over Complex Numbers

Free and online Factoring Over Complex Numbers Calculator makes your calculations and gives the factors of polynomials over complex numbers effortlessly. Just provide the polynomial in the specified input field and tap on the calculate button to get the accurate result quickly.

**Ex: **

### What is meant by Factoring Polynomials?

Factoring polynomials means breaking up the polynomial into simpler terms i.e factors when those factors are multiplied together to get the original polynomial. The different methods to factorise polynomials are GCF, grouping method, sum or difference in two cubes, the difference in two squares method, and others. To know more about factoring polynomials over complex numbers see the below sections.

### How to Find out the Factoring Polynomials Over Complex Numbers easily?

Some of the individuals may feel that factoring over complex numbers is difficult. To help you in solving these problems, we are giving the detailed explanation in the below segments. Follow these guidelines while solving the questions.

- Get a polynomial expression to find factors over complex numbers.
- Expand the expression by separating its terms.
- Take the common factor out of expression.
- So, the factors will be obtained.

As you usually can't describe the roots exactly except by saying something like "the third root of the polynomial," one normally makes do with a decimal approximation, which means you use numerical methods to find them, such as Newton's Method, or any other related method.

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### Multiplying Polynomials with Example

**Example**

**Question: Find factors over complex numbers of x³+3x²+9x+27.**

**Solution:**

x³ + 3x² + 9x +27 =(x³)+(3x²)+(-3ix²)+(-9ix)+(3ix²)+(9ix)+(9x)+(27)

=((x²)(x)+(3x)(x)+(-3ix)(x)+(-9i)(x)+(x²)(3i)+(3x)(3i)+(-3ix)(3i)+(-9i)(3i))

=((x²)((x + 3i))+(3x)((x + 3i))+(-3ix)((x + 3i))+(-9i)((x + 3i)))

=((x)(x)+(3)(x)+(x)(-3i)+(3)(-3i))(x + 3i)

=((x)((x - 3i))+(3)((x - 3i)))(x + 3i)

=(x+3)(x-3i)(x+3i)

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### FAQs on Factoring Over Complex Numbers Calculator

**1. How do you factor polynomials over complex numbers?**

To factor polynomials over complex numbers, enter the polynomial as input and hit the calculate button. You will get the given polynomial factors easily.

**2. Solve factor x²+2xi-1 over complex?**

Given polynomial is x²+2xi-1 = (x)(x)+(i)(x)+(x)(i)+(i)(i) = x(x+i)+i(x+i) = (x+i)(x+i) = (x+i)²

**3. Where can I find solved examples for Factoring Over Complex Numbers concept?**

You can find the example questions with solutions for factoring over complex numbers concept on our website along with a calculator.

**4. What is Complex Factoring?**

The algebra fundamental theorem states that polynomial with real number coefficients can be factored over complex numbers. For quadratic polynomials, the roots are complex when the discriminant is negative