Factor the gcf out of the polynomial calculator

The online factoring calculator helps to factor any expression (polynomial, binomial, trinomial). You can easily transform complex expressions into a product of simpler factors by using this calculator. If you have four terms with no GCF, then this online factoring finder calculator allows you to do factor by grouping.

Now, it’s time to give a read to get a better understanding of how to factor polynomials, trinomials, binomials step-by-step, and much more you need to know!

What is Factoring?

In mathematics, factorization or factoring is a technique of writing a number as a product of numerous factors. Usually, we multiply two or more numbers to get a final expression.

However, factor polynomials can be expressed with coefficients and they are irreducible. For example:

$$ 2 * 2 = 4 \text {or} x^2= 4$$

Similarly, Factor trinomials can be expressed as “\(ax^2 + bx + c\)”. Trinomial factorization is the technique of multiplying two binomial factors.

Additionally, binomials are the two-term expressions that connected with a plus sign or minus sign such as \(ax+b\). Remember that the first term always includes a variable, while its second term may or may not.

Well, our factoring calculator helps you to do factoring on these all above-mentioned expressions. Also, you can use an online prime factorization calculator that help to makes prime factors of any number.

Removing Common Factors:

Steps to remove the common factors are:

• Find the common factor. It can be a combination of integers and variables.
• Now rewrite a polynomial as the product of a monomial and another polynomial.
• Look for the greatest common factor. It will be a whole number.
• Now Divide polynomials by that GFC.
• Write the result in parentheses.
• Remove the common factor from the parentheses.

Example 1:

Factor \(12y^3 + 6y^2 + 18y \) ?

Solution:

$$ 12y^3 + 6y^2 + 18y = 6y(2y^2 + y + 3)$$

Example 2:

Factor \(2a – 4b + 2\) ?

Solution:

$$ 2a – 4b + 2 = 2(a – 2b + 1)$$

Factoring By Grouping:

Factoring by grouping can be done in the following steps:

• Create smaller groups of factors.
• Write factors of both groups in parenthesis.
• Find out the Greatest common factors from each of the two groups.
• Now arrange the factor of both groups and highlight what is common inside the parenthesis.
• Factoring trinomials can also be done in groups.
• A factor finder can be used for grouping the factors.

Example 3:

$$2x(y + 3) + 5(y + 3)$$

Solution:

Here \((y + 3)\) is a common factor, so we have

$$(y + 3) (2x + 5)$$

If we again multiply, we find

$$(y + 3) (2x + 5) = 2x(y + 3) + 5(y + 3)$$

Example 4:

$$3ay + 6x + a^2y + 2ax$$

Solution:

There are four terms in expression have a common factor. For example, 3 factor from first two terms, shows \(3(ay + 2x)\). Now factor other two terms we get \(a(ay +2x)\). Hence, the expression is now \(3(ay + 2x) + a(ay + 2x)\) , and a common factor is \((ay + 2x)\) and can factor as \((ay + 2x)(3 + a)\). After multiplying \((ay + 2x)(3 + a)\), we get original expression \(3ay + 6x + a^2y + 2ax\).

How to Factor Polynomials?

Factoring Polynomials is an important process that can be done by simple steps:

• For a polynomial, always check the greatest common factor (GCF) first in all terms.
• If we found the greatest common factor then factor it out of polynomial.

Find GCF is a difficult task if you want to do it manually, you can use a polynomial factoring calculator which is very efficient and error-free.

Moreover, an Online GCF Calculator allows you to calculate the greatest common factor (GCF), GCD, and HCF of the set of two or n numbers according to different methods.

Example 5:

Factor out the GCF:

$$y(3y – 1) + 5 (3y – 1)$$

Solution:

Here \((3y – 1)\) is a greatest common factor, so we have

$$y(3y – 1) + 5 (3y – 1)  = (3y – 1) (y + 5)$$

Factoring a Polynomial with Four Terms

If we have four-term with no greatest common factor then we try factoring by grouping like:

• Group only the first two terms and then the last two terms together.
• Now, factor out a GCF from each binomial.
• Find out factor common binomial.

Additionally, you can give a try to this factoring calculator that lets you solve factoring by grouping.

Example 6:

Factoring by group:

$$y^3 + 3y^2 + 2y + 6 $$

Solution:

There is not any GCF in all terms, so let’s go ahead and start factor this by grouping.

$$y^3 + 3y^2 + 2y + 6 = (y^3 + 3y^2) + (2y + 6)$$

Now

$$y2(y + 3) + 2(y + 3)$$

$$(y + 3) (y2 + 2)$$

Hence, if we multiply the answer, we get the original polynomial.

How to Factor Trinomials?

This method can’t be used all that often, but it can be used when it can be somewhat useful. This method can be done by following steps:

• Multiply two binomials
• Trinomial factoring having a 1st term coefficient of one.
• Find factor completely of any factorable trinomials.

Even though this method helps to find answers without going through so many steps, but factoring trinomials calculator helps you to find a factor of trinomials in a very simple way by just entering an expression.

However, An Online Factor Calculator helps you to find the pairs of factors of a positive or negative number.

Example 7:

Find the Product of \( (2x + 3)(3x – 4)\) .

Solution:

Multiply the first two terms of factors that are \( (2y)(3y)\), So the answer is \((6y^2)\).

Now, the product of the second terms of factors is \((-12)\) which came from \((+ 3)(-4)\).

Last but not least, the sum of two products \((2y)( -4) and (3)(3y)\).

So,

$$ 6y2 + 9y -8y – 12$$

Hence

$$(2y + 3)(3y – 4) = 6y2 + y – 12$$

When products of outside and inside terms give like terms, they can be combined and the solution is a trinomial.

How Factoring Calculator Works?

An online factoring finder calculator is 100% free and easy to perform factoring on any expressions, let’s find what you need to do:

Input:

• Enter the given expression into the designated box
• Hit the Calculate button

Output:

This factoring calculator gives you:

• Your input expression
• All the possible factors for entered expression

FAQs:

What are the 4 Types of Factoring?

The common types of factoring include:

1. Finding the GFC or Greatest Common Factor.
2. Factorization by Grouping.
3. Finding the Difference in Two Squares.
4. Sum or Difference in Two Cubes.
5. Factor the Trinomial or trinomial method.

What is the Importance of the Process of Factoring?

It is an important mathematical technique that helps you to develop a comprehensive understanding of your equations. Through factoring, you will be able to rewrite polynomials in a simple form.

What are the Key Features of a Polynomial Function?

A polynomial function will be either zero or the sum of non-zero finite numbers.

Such non-zero finite numbers will be a product of the coefficient of the term and a variable raised to some power (non-negative integer)

Final Words:

Thanks to the factoring calculator that helps you to carry out the complex process of factorization. It eliminates the need to write coefficient and exponents when it comes to finding the factorization of a trinomial, binomial, and polynomial manually. Hence, we can rely on this free online calculator for learning and educational purposes.

Reference: 

From the source of Wikipedia: Expressions, History of factorization of expressions, Common factor, Grouping.

From the source of Mesacc: Factoring Strategies, Adding and subtracting terms, Binomial expansions.

From the source of Chilli Math: Factoring Trinomial, Polynomials, Primitive-part & content factorization.

How do you factor GCF out of a polynomial?

What is the GCF of the polynomial?