# Factoring Polynomials Calculator

Factoring Polynomials Calculator expresses the given polynomial as a product of its factors. The process of decomposing a polynomial into a product of two or more polynomials is known as factoring polynomials.

## What is the Factoring Polynomials Calculator?

Factoring Polynomials Calculator is an online tool that breaks up a polynomial into the product of its factors. Factoring can help to simplify a polynomial and increase the ease of performing calculations using that polynomial. To use this **factoring polynomials calculator**, enter the polynomial in the given input box.

### Factoring Polynomials Calculator

## How to Use Factoring Polynomials Calculator?

Please follow the steps below to find the factors of the given polynomial using the online factoring polynomials calculator:

**Step 1:**Go to Cuemath’s online factoring polynomials calculator.**Step 2:**Enter the polynomial in the given input box of the factoring polynomials calculator.**Step 3:**Click on the**"Solve"**button to find the factors of the given polynomial.**Step 4:**Click on the**"Reset"**button to clear the field and enter new values.

## How Does Factoring Polynomials Calculator Work?

The steps to factor a polynomial are as follows:

**Step 1:**Check if there is a factor that is common to all terms of the polynomial. If yes, factor it out and then move to step 2. If no, move on to step 2.**Step 2:**The appropriate method (grouping, splitting the middle term or using algebraic identities) needs to be used for factoring the given polynomial.**Step 3:**Finally, express the polynomial as a product of its factors.

Given below are the different methods used to factor a polynomial.

**Common Factor Method**- In this, the common factor of all terms is factored out to simplify the given expression.**Grouping Method**- In this, we find groups of factors that are common to certain terms of the polynomial. These are factored out to simplify the polynomial.**Splitting the Middle term**- This method is usually used for quadratic polynomials. In this, we split the middle term as the sum of two factors. We also express the constant term as a product of these two factors. Finally, this expression is simplified.**Using Algebraic identities**- We take the help of algebraic identities to simplify the given polynomial.

## Solved Examples on Factoring Polynomials

**Example 1:** Find the factors of the polynomial 3xy^{2} + 5x^{3} - x^{2}y and verify it using the factoring polynomials calculator.

**Solution**:

Given: Polynomial = 3xy^{2} + 5x^{3} - x^{2}y

x is common to all terms thus, we factor it out.

= x ( 3y^{2} + 5x^{2} - xy)

**Example 2:** Find the factors of the polynomial x^{2} - 2x + 1 and verify it using the factoring polynomials calculator.

**Solution**:

Given: Polynomial = x^{2} - 2x + 1

Using the algebraic identity, (a - b)^{2} = a^{2} - 2ab + b^{2}

x^{2} - 2x + 1

= x^{2} - 2. 1. x + 1^{2}

= (x - 1)^{2}

Now, try the factoring polynomials calculator and find the factors for:

- x
^{3}+ 5xy + 6x + 5 - x
^{2}- 5x + 6

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