Thursday, November 9, 2017

All about Factorization

It is always better to start from scratch and know how the process in-built together and incorporated at places than to start working and return back to the basics.

What does the term Factorization mean?
It is the process of finding out factors of a polynomial or any equation. It is moreover like splitting of a complex term into two other numbers whose multiplication product if equal to the main term.
It can also be defined as the decomposition of a mathematical equation and is not necessarily applicable to polynomials, but also for Matrices and numbers

Why should one Factorize?
The main objective of factorizing is to reduce the complexity of the problem. The end results of Factorizing are something which cannot be further divided, thus breaking the equation to its simpler form.
The factorizing terms in their form can further be multiplied again to retain the original equations. This is also known as the expansion of polynomials. It is the best way to verify the solutions obtained after the factorizing process.

Equation
Equation

When should we Factorize?
Before moving on to factorization let us have a look at the factor theorem:

The factor theorem states that when a polynomial f(x) has a factor that is (x-k), it is only when f(x)=0
This means that the value of k that is obtained is a root of the polynomial.

Other uses of the Factor theorem are:
The factor theorem is used to remove known zeros from a polynomial while leaving all unknown zeros fixed, thus producing a lower degree polynomial whose zeros are easier to solve.
The method is:
1.    Use the factor theorem to conclude that the term (x-a) is a factor of f(x).
2.    Solve the polynomial g(x) =f(x)/f(x-a), for example using Long Division method of Polynomials or Synthetic Division method.
3.    Say that any root x is not equal to an of f(x) =0 is a root of g(x)=0.
4.    Since the polynomial degree of g is one less than that of the degree of f, it is "simpler" to find the remaining zeros.


Few Common Methods of Factorization
Listed below are the few commonly used methods for factorization:
Let us have a quick look at them

1. Highest Common Factor
The highest common factor of algebraic expressions is useful in factorization; and it is the product of the common prime factors, which includes both common numerical and algebraic factors.

2. Using the Common factor
ab+bc= b(a+c)

3. Using the Difference of the square formula
a^2-b^2= (a+b)(a-b)
By using the above method, you can easily find the factors of a number.

Real Life applications of Factorization

Finance
Commonly used in finance and accounting where the present value of the assets are determined and for stock evaluation. Its uses are also traced in bond trading and calculations.

Numerical Analysis
For complex and high ordered equations in derivations and formulae method of factorization is needed to reduce the complexity of the problem, thus getting a valid solution or a better and simpler form of the equation. Also, high tech algorithms use the basics of Factorizing.

Quadratic equations

Integration sums and wave equations always end up unexpectedly in a quadratic form and then the only factorization can reach for your help. It is also widely used for solving numerical and calculation unknown values when in higher than or equal to 2nd order format.

Saturday, October 21, 2017

Solve Quickly any Parabola Equation via Online Math Software

Mathematics is an interesting subject, but not for all. Those who are weak in mathematics find it difficult to pass the examination. And as the level goes up topics become challenging, and students look for different options to take help. They seek help from tutors, online tutorials, reference books, etc. to get the answer to the challenging and tricky questions. Not every book contains the good explanation of the question and that to be step by step. Some books give the only short explanation of question which is not sufficient to understand the solution. Keeping this in mind online math solver software developed to help and guide students in mathematics. The software can solve any equations like quadratic, polynomial, parabola, etc.
Parabola
Parabola

Students can get help from this software, they are online, and there is no need to download any pdf or video to watch the solution. Some software gives solutions of any specific problems like the parabola or any other. Using them will not help you in solving other topics; hence you must use one who can assist you on every topic. Step by step description of any question is given, and students can note it down to practice such type of questions.
For example, you are solving a quadratic equation, and you are not getting the values of variables. With the help of math solver, you will not only get the values, but it will also plot a parabola graph with the accurate focus, vertex, and directrix. Parabola is a symmetrical curve of U-shape, every point that lies on the parabola is at equal distance from the focus and directrix. The curve corresponds to a quadratic equation. The point from where parabola makes a turn is called as the vertex. It lies between focus and directrix.

How to use the calculator for solving parabola equation?
It’s simple, just follow the steps.
        Open the online math software
        You will see a calculator just like regular calculator
        Enter the parabola equation in the box.
        Click on simplify button
        You will see step by step solution
        Click on steps to get the detailed explanation

Although the description is given in simple steps, if you want to learn from the experts then watch the online video. There the expert teachers will teach you in the best way. This software is free to use, and you can use it without any difficulty. However, you may have to register on the site so that they can help you more efficiently. Once you registrar you quickly use the rest of the services. You may not get an explanation of entire solution until you register, hence to see the full description first register.


Many such online types of software are there to help the students, but not all provide you the correct answer. Hence comparison is a must. So before using any such software to solve tricky equations like parabola must compare the accuracy of the solution. To make you understand many examples of similar questions are given on the software, refer them to solve the one in which you are getting the problem.

Wednesday, October 18, 2017

Is multiplying fractions is your problem? Use online software

Many students get stuck in between while solving an equation that contains fractions. Those who are new to this concept will face the problem, but with practice, they can master it. However, after learning so hard many students still experience difficulties in multiplying fractions. Multiplying fraction is simple than addition or subtraction. But still few are not able to solve them, and the only reason is that their concepts are not clear. By learning the basic idea, anyone can answer any tricky question with ease.

While solving the equation, you may have to multiply mixed or whole numbers. Multiplication is simpler because unlike addition or subtraction you don’t have to get the lowest denominator that is common in both fraction values. By following four simple steps, you can multiply fraction easily.

Steps to multiply fractions-
        Convert mixed number into improper fraction
        Simplify by canceling the terms
        Multiply numerator and denominator values
        Again convert back the improper fraction into a mixed number.
Young learners should remember the above steps for multiplying fractions. If you still don’t understand how to apply these steps then watch the videos on the internet. Get step by step explanation from the video along with an example. You can also take help from the software that is only designed to solve tricky mathematics question. The simple description along with easy to hard examples is explained. The software gives the Quick solution, easy description, an alternative method to solve the question. They are accommodating during the examination because that time you need a quick solution. So, rather than searching the problem in the book, get the answer online within few minutes.

Math is fun and to make the student understand this software give an easy explanation. No matter how tricky the question is, you will get an accurate answer. From the simple calculation of addition and subtraction, solving algebra, multiplying fractions, etc., there is nothing that it can't-do. Students of any age, any class can use them and learn mathematics topic with ease and fun. At the site you will get the list of different topics, select according to your choice and learn the basics of the topic. It will provide the solution of the word problems also. Just enter your email, then question and get the answer.

Multiplying fractions was never that tough and with the help of online software for math students can take their learning to the next level. They will not only excel in school exams but also in other competitive exams. The way they teach is very effective, and you will never forget the basics. Because basic is the foundation and if you know the basic of multiplying fractions then you can solve difficult questions very quickly.

        You can get solution of any problem from your textbook
        Ask if you don’t understand any step
        Watch the answers online through video classes
        Get 1000 of problems with solution to know in how many ways question can be asked
        Solve word problems of any type for example coin, mixture, age, etc
        Learn multiplying fractions
By using online math software, you can improve your mathematical skills and get the good knowledge of the concept.

Wednesday, October 4, 2017

Why Solving Algebra Equation can be Hard for Some Students

It is not easy to learn algebra even of the students who are the bright. Most of the time, the students regardless of which level they are on, they will want to review the algebra concepts while preparing to get advanced courses like calculus.  Algebra is also an integral part in doing some standardized test such GRE.  When it is about the algebra and pre-algebra, solving the unknown factor can turn to be intimidating for the students who have been used to perform the straightforward operation.  The complex happens when there will be confusing symbols that can seem to be a foreign language.  However, when the students get to understand more about the algebra equation language, they will succeed in doing algebra.  It is good to build the understanding from the start, and the student will stop to see algebra like the system of the arbitrary rules, but as a language, they are able to understand. Algebra does not have to be a cause of the frustration, and when the right tools are used, the student may learn more on how they may approach an equation and to solve it in the correct manner.
Algebra Equation
Algebra Equation

When a student struggles with algebra, it is good to evaluate his learning problems and to know the best way that she can learn. You have to know also the obstacles that interfere with the performance, if it is a lack of the attention in the class or if it is a trouble to get the help. It can also be a poor grasp of the basic concept or the need to get visual learning tools.

Since algebra or pre-algebra will lay the foundation to understand the advanced math course, it is important that every student understand the concept.  All the algebra equations depend on the previous rules. If the students have some holes in the understanding algebra, they may have a hole in how they understand the entire subject.  When students fail to understand something, they will end up assuming that the entire process is hard and they will resist learning more in the future.   When a student performs badly or answers wrongly, then he may suffer a chronic under performance because he will lose self-esteem.

The students may also fail because their teacher does not have the right materials or the right skills. Sometime the students may also be embarrassed in asking the teacher about what he had taught.  If the student is liberated away from the classroom pressure, they will start to find that math is easy and they will learn better.

Getting the help in math; helps to fill the gaps to ensure that the comprehension will fall in the place naturally.  You should get the teacher who has experience in explaining the even difficult concept using simple language. The students should have a comfortable environment where he will not feel embarrassed.  The algebra equation has to be presented in logical and organized manner. The best tutor or educator will supplement the learning using colorful diagrams and graphics. 

Friday, September 1, 2017

How to Factor the Quadratic Equation to know Variable Quantity?

An algebraic equation is one of the common math problems which include linear, quadratic and other higher degree equations. Solving out these equations is difficult sometimes due to the tough coefficient. If your kid is facing any difficulties in solving the algebra homework, then you can help by knowing the easy method for its solution. You can access the digital platform in which you just have to enter the coefficient then you can achieve the variables.
Without the graphing calculator or algebraic calculator, it is difficult to solve but it is not so. You can use the formula method or use the factors to determine the variable values. How to factor is the most common question that would come to the mind of the learner.  

Quadratic Equation
Quadratic Equation

How to solve the quadratic equations?

Before solving the quadratic equation, you should understand its basics. To understand the quadratic equation, consider an example as- 2x² + 6x + 9 = 0 

A quadratic equation is written above in which x is the variable, and the number with X is coefficients and remaining one is constant. To get the math help by the calculator, you just have to fill the coefficient and constant values into the software. You can easily get the variable value which may be negative or positive. On the other hand, you can use other methods. These methods are as-

Solve by formula method 

A and B are the coefficients of   and x respectively, and C is the constant value available in the algebraic expression. Here in the equation, you have  
A= 2
B = 6
And c = 9

Now put the value into the equation, you will get,
After solving the numerical expressions, you can get two values. One is negative, and other one is positive.

By Factor method
Factor method is nothing but breaking out the expression into two parts i.e. taking out the common factor from the expression. Also, it is the simple and fast method to get the variable values. In this method, you don’t need to remember the complex formula. To better understand the factor method, you should know how to factor the expression. Consider an example to understand the factor method better and solve the quadratic algebraic equation.
2x² + 6x + 9 = 0

Follow the steps-
2x² + 2x + 3x + 9 = 0
In this step, the central part is divided into two parts
Now, you have to select the common factor out, i.e.
2x² + 2x + 3x + 3 = 0
2x(x + 3) + 3(x + 3) = 0

Take out the common factor again,

2x(x + 3) + 3(x + 3) = 0
(x + 3) (2x + 3) = 0
Now, you have two factors i.e. (x + 3) and (2x + 3)

Keep both the factors equal to zero to achieve individual values
X+3 = 0
X = -3
Again,
2X + 3 = 0
2X = -3
X = -3/2

We have two values of X which are determined by the factor method i.e. X = -3, -3/2

By this method, we do not have to face any complex calculations as faced in formula method. Here the most complex calculation is to choose the common factor. Also, you can find the simple method, but these methods are best to get the accurate answers. To check the answer, you can put the variable value into the expression. If the quadratic equations become zero, then you have right variable values.

Tuesday, July 18, 2017

Learn the most Basic Steps for Solving an Algebra Equation

Mathematics has been one of the most interesting subjects among the learners. There are numerous interesting topics that are available for the learners of mathematics. One of them is solving an algebra equation. There are many important concepts that need to be understood and many other methods that need to be learned in this respect. There can be many easy ways through which the beginners can become perfect in solving a linear equation. Understanding these would help the readers to get better at them. Therefore we are going to discuss some most common and interesting facts about the steps involved in solving linear equations.
Algebra Equation
Algebra Equation

Let’s understand better
Linear algebraic expressions can be said to be the equations with any common variable like “x”. However, these do not have anything complicated like x⁄y or x² . Therefore these are much easier to solve than any other equations you may have. There are no square roots or anything more; there are just simple variables and operations. So if you are looking out for such simple equations then relax for you will be able to complete your algebra homework on time.  Solving simple equations is just like the ‘fill in the block’ exercises in your early schooling years. However here you need to ascertain the exact value that will be working in place of the variable “x”.

You may get to learn more advanced methods in respect of solving these equations. The first and the most important this that you need to know in this respect is to separate the variable from the other part of the algebra equation. For this, you may also need to consider the rules of LHS and RHS. This way you will be able to bring in the answer i.e. the correct value of x. Let’s understand this with an example. For example, the problem is: 
Solve x+9 = -30
Now the main thing you need to ensure is to isolate x from the other contents in the equation. The next will be: x =  -30-9 ;
When you bring 9 to the other side in order to separate x from the equation, you need to focus on the sign change. You need to perform exactly the opposite operation in order to simplify the equation. Also, you need to consider the negative sign with 30. This is important as it will play a major role in getting the solution. The digit 9 which is added on the left side will now be subtracted when it moves to the right. So now the solution for x is simple.
x = -21

Thus it is very easy to solve linear equations. However, there are many other methods that you need to learn and can be applied to get the right answers for these equations. But this is the basic rule that you need to follow in respect of all types of equations. Therefore now you can easily try to complete your algebra homework. A bit of practice will always be the best to make you perfect for solving algebra equations without any help. Also, it will always improve your perfection.

Saturday, July 1, 2017

How to Solve Quadratic Equations within Seconds?

A quadratic equation is a polynomial equation which includes a variable with a high degree. In algebra, the equation includes some numbers and a variable. The value of a variable is lies between the quadrates. The number of values of the variable is completely dependent on the degree of it. If the equation includes a higher degree of two than there are 2 values are available of unknowns. To solve quadratic equations, you need to follow some rules, but it usually takes more time. In competitive exams, the time plays an important role to qualify it. We cannot spend a lot of time on single questions. That is why it is best to know the tricks to solve quadratic equations.
Before going to solve any example, first, understand the basics of it,

Consider some example like 
In the first equation, the higher degree of a variable is 2, and in the second one, the higher degree is 3. So we may get the value of x 2 and 3 respectively.

The standard form of quadratic equation is  ax²+bx+c=0
So, we can find out the value of x by the formula as, X =  

If we consider the second 2x³ +12x +8=0 then it can be solved by above equations

The values a, b and c According to the standard form of a quadratic equation, the value is found as compare both standard and question questions.
After comparing the equation we have a = 2, b = 12 and c = 8
Put the values of a, b, and c. You will get the value of x. The positive and negative sign shows two values of the single variables. 

                                                   = (-3±√80)
Now you have two values of x that is positive (-3+√80) and (-3-√80)
But it is the complex method to solve the equation and takes a lot of time to solve quadratic equations. If you need to solve these equations in the least time duration or within a minute, then use some tricks. The trick can help you to solve it in the least time.
First consider there some sign to get their answers.
If you have equation like
    ax² + bx + c= 0
    a+ bx -c= 0
    a- bx + c= 0
    a- bx –c =0 
Consider these signs to know their value signs.
First equation variable values include (-, -)
2nd includes (- , +)
3rd includes (+, +)
4th includes (+,-)
Consider an example to understand this trick to solve quadratic equations.
x²+5x-3=0
Now find the coefficient by multiplying x²and 3 coefficients.  2x3 may write as 6x1, and the result will be achieved by 6 and -1
The final root may divide by the 2 which is the x² coefficient. 
Now you have 6/2 and -1/2
You have roots (3, 0.5)
But the sign shows (-, +) and according to the trick you must have root (-3, 0.5)
This is a very short trick to get the root of unknown variables. The trick needs to only 30 to 60 seconds to solve quadratic equations. If you are looking the best method to solve quadratic problems in less than a minute then must apply this trick which requires least time.