How to solve factoring polynomials? Learn three ways to do

Factoring is essential to simplify the algebraic expressions. This topic is very useful for the students as without understanding the basic of factorial polynomials one would not be able to understand the later topics. Many students often confused between the factors and term, they think both are same, but no they are not. In any equation, we can add or subtract a term whereas factors need to be multiplied. You can understand them through their definitions.

Definition of factor and term:

A term can be added or subtract whereas when we multiply a term, then it is called as the factor. If the entire term in an equation is in product form, then it is a factored form of an equation. A term may or may not contain factors whereas a factor is made of a term. We can change the term into factor form by changing the expression into product form. However, remember that terms or value doesn’t get changed only its form gets manipulated.

For example- 3x(x+y) is an expression in factored form and3x+4y+z is an expression in non-factored form.

How to remove common factors?

Here you will learn how to get common factors and greatest common factor. To learn, let us take an example.

 Example – Factor 2×2+4xy+8xy2

Solution- first we will take out the factors for each term

The factors of 2×2 are 1, 2, x, x2, 2x and 2x^2

The factors of 4xy are 1,2,4,x,y,2x,4x,y,2y,4y,2xy and so on

The factors of 8xy2 are1,2,4,8,x,y,2x,4x,8x,xy,xy^2 , 8xy^2 and so on

Take the greatest common factor from these. Out of these, the H.C.F is 2x. Now divide the whole term by this factor. You will get-

2×2+4xy+8xy2= 2x(x+2y+4y2)

Check the correctness by solving the equation on another side, and if the L.H.S is equal to R.H.S, then it is true.

How to find greatest common factor using grouping method?

This method is not very popular, but it is quite useful when used.

Example- 2x^2-x+8x-4

Group the first and second terms, and you will get the two groups as shown here,

= (2x^2-x) + (8x-4)

=X (2x-1) +4(2x-1)

The common factor is 2x-1, the final factor form is 2x^2-x+8x-4= (2x-1) (x+4). Note that this method doesn’t work every time, and hence you cannot use it to solve every problem.

How to factor quadratic polynomials?

The quadratic equation is nothing but a second-degree polynomial, so the highest degree of expression will be 2. When finding factoring polynomials, you need to find a term which when multiply gives the third term of expression and when added gives the second term. If this condition is not satisfied then obtained factors are incorrect. It is easy to find the factors for some equations whereas some complex quadratic expressions do not give factors. In such situation, we use the quadratic formula.

How to find factor for equations with the higher degree?

To solve such problems, take the common factor from expression and use the above methods to get the factor.

Example – 3×5+3×4-9×3+18×2

Solution- the common factor is 3×2, so we can write the expression as 3×2(x^3+x^2-3x+6) to solve further use any of the methods above.


Various Tools to Solve Greatest Common Factor Problems Easily

Most of the students find math very difficult subject due to lots of formula and equations but in fact math is very interesting subject to learn new things. If you are also one of those students who find the math hard to learn, you can get help of technology to make it easy. Technology is making it possible to solve the math problems easily by using short cut methods. The students can use various online tools and computer software to get help to solve the math questions.

Online tools to solve these math problems:

If you are also looking for such solution, you can get help to solve the greatest common factor problems. The online tools are free to get and anyone can use it to get help in math problems. If you also want to use these tools, you can use in any device. Whether you have any computer or smart phone, you can use these online math solving tools. By using the math solving tools, students will get problem of all problems of algebra, numbers, equations, matrices and other categories. So it is best option that you can get the online tool to solve desired math questions.

The best thing about these tools is that students can use the tool in different devices running on different platforms. It is perfect option to save time in getting solution for math problems. You can also use other tools to solve problems of greatest common factor. Lots of tools are available for computers and smart phones that can be used to solve various math problems.

Use online tools easily for different questions:

It is very essential that the online tools have simple and easy to use interface because different students will use it. If you are using the online math solver tools, you will get very user friendly interface. The students just need to choose the topic of math from various categories like algebra, numbers, equations, matrices and greatest common factor. Then you can get the instant solution by putting the question of math. These tools use simplest and short methods to solve these questions.

The online math solving tools are not only made to provide quick solutions but the students will learn new solutions for various problems. In exams, the students need simple and short methods to find quick solutions of math problems. These tools are made in a way that you can learn easiest process to find the answer of various meth questions.

Every topic of math is based on the formula. The students, who are unable to learn these long formula of different topics, can easily find short and alternate formula from these kinds of tools. These are best methods to add some fun while learning the math. They are making it effective for all kinds of students who face problems to learn the math topics. Every student will find these tools effective and easy to use to find proper and easy solutions for various math topics and questions.

How do you Find the Greatest Common Factor

The greatest common factor is also called as the Greatest Common Divisor GCD or Highest Common Factor HCF. It is the factor that divides two numbers. The greatest common factor can be found by listing of the prime factors of each of the numbers; then these factors need to be multiplied by the numbers that both have in common. Incase there are no common prime factors then it means that the greatest common factor is 1.

Greatest Common Factor
Greatest Common Factor

For Example, the greatest common factor of 9 and 12 can be denoted as
The Prime Factors of 9 which are 3 x 3
The prime factors of 12 which are 2 x 2 x 3
Therefore the common factor is 3 which make the GCF 3
The Greatest common factor is used for finding the largest factor which is used to divide two numbers.
In order to find the GCF of 15 and 60
The prime factors of 15 are 5 x 3
The prime factors of 60 are 5 x 3 x 2 x 2
Therefore as 5 and 3 are common, the GCF is 3 x 5 or 15

When Finding the GCF there are 2 Methods:
a) First, the common factors need to be compared. Then the sets of factors need to be compared till the biggest number which is in both sets is identified.
b) The second method is the prime number method. In this, the factors of each number first need to be broken into the prime numbers. Then common prime factors need to be picked out. After which all the common prime factors need to be multiplied, and that is how you arrive at the greatest common factor.
The Greatest Common Factor in a polynomial needs to be checked as factoring of the polynomial is easier when the GCF is factored. The terms get less cumbersome. Incase the GCF has a variable, it gets easier.
Incase there is a polynomial equation 6y4-12y3+4y2 these are the steps to be followed:
The terms are to be broken into the prime factors which are
(3 x 2 x y x y x y x y)- (2 x 2 x 3 x y x y x y) + (2 x 2 x y x y)
Then the factors which are in every single term should be determined. In the above example, the common factors are 2y2
The GCF is then to be factored out and placed in front of the parenthesis and then the remnants are to be grouped inside, so it will be 2 x y x y (3 x y x y – 2 x 3 x y + 2)
Then the 2y2 is to be multiplied to each of the factors inside the parenthesis to check and see if the GCF calculated is correct.
This is how GCF is calculated. The GCF is used for all kinds of calculations including for working with fractions. Therefore, this is a concept which needs to be thoroughly understood.