Polynomial Factoring Calculator

By: Tasha Kolesnikova

9 min

5

10.04.2022

Every student has to solve math assignments at some point in their academic life. The Factoring Polynomials Calculator is an application that performs as an algebraic expressions/ algorithm solver and displays the polynomial expression's factors (factor x) in a short period. The factor calculator will factor any polynomial (binomial, trinomial, quadratic equation, etc.) with a step-by-step solution.

Online calculators can perform various functions to solve math problems in today's digital world. The factor expressions equation calculator can be used for factoring trinomials, factoring quadratics, grouping and regrouping, square roots, the cube of sum/difference, a difference of squares, perfect squares, and the rational zeros theorem.

What Are Polynomials?

Polynomial is made up of two words: Poly (which means "many") and Nominal (which means "terms.").

Polynomial

Polynomial — is a mathematical equation made up of variables, constants, and exponents mixed using operations like addition, subtraction, multiplication, and division - no division operation by a variable.

Variables and coefficients make up polynomials, which are algebraic expressions. Indeterminates are another word for variables.

The word polynomial comes from the Greek words "poly," which means "many," and "nominal," which means "terms," therefore it means "many terms." A polynomial can have many terms, but it cannot have an infinite number of terms. It is classed as monomial, binomial, or trinomial based on the number of words in the phrase. The following are some examples of constants, variables, and exponents:

1. Constants: Examples of constants are 1, 2, 3, 4, 5, etc.
2. Variables: Examples of variables include a, b, c, d, e, etc.
3. Exponents: Examples of exponents are shown in the following image:

Symbolism

P(x) denotes the polynomial function, where x is the variable. The function will be P(a) if the variable is designated by a.

A Polynomial's Degree

The highest degree of a monomial within a polynomial is the degree of a polynomial. A degree of the polynomial is a polynomial equation with one variable that has the greatest exponent. For instance, in the exponents' examples above, the degree for the first example is 5, and for the second example, it is 1/n.

Terms in a Polynomial

Polynomial terms are the components of the equation that are usually separated by"+" or"-" marks. As a result, each term in a polynomial equation is a component of the polynomial. A polynomial's classification is determined by the number of terms it contains. For instance, in the example below, the number of terms in the polynomial is 4.

Different Types of Polynomials

Polynomials are grouped into three categories based on the number of terms they include. The following are the three types of polynomials:

Monomial: An expression with only one term is called a monomial. The single term in a monomial expression must be greater than zero. The following are the examples of monomials:

• 4a
• 83x
• -7xy

Binomial: A binomial expression is a polynomial expression with precisely two terms. A binomial is defined as the difference or total of two or more monomials. Examples of binomials are:

Trinomial: A trinomial is a mathematical expression that has precisely three terms. Here are some instances of trinomial expressions:

Addition, subtraction, multiplication, and division can be used to combine these polynomials. However, division by a variable is never used.

Factoring Polynomials

Factorization of polynomials is the opposite of multiplying polynomials by their factors. If we divide a polynomial by any of its factors after being factorized, the residual will be zero. We also factor the polynomial by determining its largest common factor throughout this operation.

Factorization is the process of identifying factors for a given value or mathematical equation. The integers that are multiplied to generate an original number are known as factors.

Polynomial Factoring Types

Factoring polynomials may be done in six distinct ways. The following are the six methods:

• GCF or the Greatest Common Factor
• The Grouping method
• The Difference in Two Squares Method
• The Sum or Difference in Two Cubes
• General Trinomials
• The Trinomial Method

We can factorize polynomials using generic algebraic identities in addition to these approaches. Similarly, we may use the quadratic equation to identify the roots or factors of a given expression if the polynomial is a quadratic expression.

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I studied sociology and marketing at Europa-Universität Viadrina (Germany) and Universidade da Beira Interior (Portugal). When I was a sophomore, back in 2018, I decided to put what I've learned into practice, so I got my first job in digital marketing. I currently work in the content marketing department at Studybay, building strong, effective, and respectful communication between the platform and our clients.

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• I really enjoyed learning about the origins of the word in your article. Knowing that it roughly translates to "many terms" in Greek makes its meaning so much clearer. Connecting the vocabulary to its roots helps me remember concepts better.👍

Fabio Conway

02.23.2024

• You explain concepts very clearly. As someone who has always struggled with factoring polynomials, your article made feel like it finally clicked! Love how you take the time to explain the why behind each step.

Haydn

03.13.2024

• The polynomial factoring calculator you included for quadratic equations is so useful! It will help me check my work and ensure I fully factored my quadratics. Thanks for adding this cool tool.

Hussein

03.08.2024

• I appreciate you covering the common methods for factoring - like grouping and trimonial methods. The tips on avoiding errors would also come in handy, I think you should add those to the article!

Kiran

02.08.2024

• Nice guide on factoring polynomials! Breaking it down into linear, quadratic, and other types makes it very easy to digest. The examples really help reinforce the different methods too.

Lydia Moreno

02.02.2024

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