  \$20 Bonus + 25% OFF

#### Polynomial Factoring Calculator with explanation

Referencing Styles : MLA | Pages : 1

Ans: Factoring of a polynomial function is one of the most important technique used in several mathematical applications like root finding, partial fraction method, stability analysis by pole zero calculation and more advanced applications in engineering and science. A polynomial is defined as a function of one or more variables containing higher powers of those variables only. For example, f(x) = x4-16 is a polynomial of degree 4 of variable x. factoring the polynomial is a process where the function is represented as a product of two or factors. It is similar to factoring of a number as a product of smaller numbers or primes, the only difference is that each factor is an expression of the variable instead of just a number. As an example the above function can be factored as (x2+4)(x+2)(x-2). This is called positive prime factoring that is the factoring process goes on until all the factors become positive primes. There are total six types of factoring which are Greatest Common factor method, Grouping, Difference in two squares, sum or the difference in two cubes, trinomials and general trinomials respectively.

Greatest common factor method: This is one of the most used factoring technique as this occurs in many other types of factoring method. In this method the largest common divisor of all the terms in a polynomial expression is taken common from the expression and represented as a factor. For example if (7x – 56) is required be factored then the GCF of the two terms 7x and 56 which is 7 is taken common from the two terms and then expressed as factors.

Hence, (7x-56) = 7(x-8)

Another example:

Factoring  =15x5+20x2+60x=5x(3x4+4x+12)

Grouping: In many cases there is no whole factor common in all the terms of an expression but there is a common factor in some terms. In that case the terms with common factors are grouped together and then the factor is taken out from those term and finally the resultant expression is expressed as product of sum form.

Example:

Factorizing the expression 3ax + 6ay + 4x + 8y.

3ax + 6ay + 4x + 8y = 3a(x+2y) + 4(x+2y) = (x+2y)(3x+4)

Factorizing 12cx + 2y + 3x + 8cy = 12cx + 8cy + 3x + 2y = 4c*(3x + 2y) +1*(3x + 2y)

= (4c + 1)(3x+ 2y)

It is seen that the terms inside each of parentheses set are the same and thus this term becomes the greatest common factor.

Difference of two perfect squares: It is represented as a difference of two terms and magnitude of both terms are perfect squares. The factoring of this type of expression gives two binomials of which one contains the sum of two terms and the other term contains the difference of two terms.

As a generalized expression a2-b2=(a+b)(a-b)

Example:

Factorizing Factorizing Sum or difference in two perfect cubes: This is factorizing difference or sum of two cubical terms. The sum formula of two cubes is given by, The difference of two cubes is given by, The SOAP acronym is commonly used for remembering the arrangement of the signs.

Here, S represents that the sign between the two terms in the binomial expression in the factorized form will be same as the sign which is given in the problem.

Example:

Factorizing X3-64

By the difference formula of the cubes it is known that in the answer term there will be the difference between the cube roots of the two terms. Next, the other factor in the answer will contain two square terms of the two terms in the expression and the multiplicand of the two terms. Now, 64 is a perfect cube of 4, hence, the answer becomes

Hence, Factorizing  = Trinomial: Before factoring the trinomial expression the terms of the expression must be arranged in a descending order. In most cases the trinomials are product of two binomial expressions.

Example:

Factorization of the expression X2+7X+12

The terms are already in descending order. Then the following process is followed. Factorization of  -16X-2X+3X2

At first the terms are arranged in descending order.

Hence,  General trinomial: In a general trinomial the coefficient of the first term cannot be factored from the GCF and hence trial and error method is used to determine the factors of the trinomial expression.

Example:

Factorizing  Factorizing -4X2+23X+6

At first the negative sign is taken common from all terms. In the simplest case the most common technique is to take common from series of terms (GCF method) and if there is no common in all terms then the later methods are applied. This GCF method is also known as un-distribution as the distribution law is applied in reverse.

Special case: trinomial of perfect square

A trinomial of perfect square is an expression which can be expressed as square of some expression or basically the expression can factored in two same factors only. In general the perfect square trinomial is expressed as Example:

Factorize OR

### Save Time & improve Grade

Just share requirement and get customized Solution.  Orders

Overall Rating

Experts

### Our Amazing Features #### On Time Delivery

Our writers make sure that all orders are submitted, prior to the deadline. #### Plagiarism Free Work

Using reliable plagiarism detection software, Turnitin.com.We only provide customized 100 percent original papers. #### 24 X 7 Live Help

Feel free to contact our assignment writing services any time via phone, email or live chat. If you are unable to calculate word count online, ask our customer executives. #### Services For All Subjects

Our writers can provide you professional writing assistance on any subject at any level. #### Best Price Guarantee

Our best price guarantee ensures that the features we offer cannot be matched by any of the competitors.

### Our Experts      5/5

440 Order Completed

99% Response Time

### Jack Arens

#### London, United Kingdom      5/5

154 Order Completed

97% Response Time

### Harold Alderete

#### London, United Kingdom      4/5

1309 Order Completed

100% Response Time

### Gemmie Chen

#### Singapore, Singapore      5/5

203 Order Completed

97% Response Time

### FREE Tools #### Plagiarism Checker

Get all your documents checked for plagiarism or duplicacy with us. #### Essay Typer

Get different kinds of essays typed in minutes with clicks. #### GPA Calculator #### Chemical Equation Balancer

Balance any chemical equation in minutes just by entering the formula. #### Word Counter & Page Calculator

Calculate the number of words and number of pages of all your academic documents.

## Refer Just 5 Friends to Earn More than \$2000

1

1

1

### Live Review

Our Mission Client Satisfaction #### User Id: 583196 - 19 Jan 2021

Australia

WHAT AN FANTASTIC OUTCOME I RECEIVED!! My essay subject was very difficult with many parts! My MAH\'s expert NAILED IT!!!! thanks a million! I WILL BE BACK! #### User Id: 383727 - 19 Jan 2021

Australia

It was a very well done job. The writings are accurate and supported with reliable resources which were related to the assignment. It was done on time and quick service. #### User Id: 552330 - 19 Jan 2021

Australia

Hi, Received the grades for this assignment this morning. Good grades with some minor feedback. Professor is happy with the content, referencing and especially the way assignment was written. Please pass on my thanks and regards to the expert who did... #### User Id: 525764 - 18 Jan 2021

Australia 