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 Calculator

Example 1:

Find the factors of the polynomial 3xy² + 5x³ - x²y and verify it using the factoring polynomials calculator.

Solution:

Given: Polynomial = 3xy² + 5x³ - x²y

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

= x (3y² + 5x² - xy)

Example 2:

Find the factors of the polynomial x² - 2x + 1 and verify it using the factoring polynomials calculator.

Solution:

Given: Polynomial = x² - 2x + 1

Using the algebraic identity, (a - b)² = a² - 2ab + b²

x² - 2x + 1

= x² - 2. 1. x + 1²

= (x - 1)²

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

• x³ + 5xy + 6x + 5
• x² - 5x + 6

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