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.

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Why do you need the Quadratic Formula Calculator?

The quadratic formula calculator has unique ways in calculating the equation.  It can solve the second order for the polynomial equation like ax2+bx+c=0   by the use of quadratic formula. The calculator solution shows the work by the use of the quadratic formula, and it solves entered the equation for complex and real roots. The calculator can determine if the discriminate is equal, greater or less to zero.

quadratic equation calculator
quadratic equation calculator

You can also find the quadratic formula calculator which shows how the formula has been used.  You can still use the graphing calculator if you want to solve a quadratic equation and even for these of the imaginary solution.

Because many people now want to work faster regardless of the field they are in, they choose to use an online calculator instead of counting manual. The calculator can solve the entire complicated problems faster and using efficient manner. The calculator will give accurate results compared to counting the equation manually. The calculator knows the formula to use, and it makes counting process easier. You can avoid boredom when you are getting the solution to the certain equation.

The calculator that was used before were limited, but this is no long the case since with technology and economy, the calculator are advanced, and people can get exact results for the problem they have. There are some functions like divide, multiply, minus which had been developed. The quadratic formula calculator is a complicated calculator, and it has been programmed to work on high-level equations.  The newest calculator is known as the scientific calculator, and it is being used in the companies and universities in order to ease the entire calculation process.

The quadratic formula calculator has anything you want in the calculator like binary functional, trigonometry, factorials, square root and the base 2.

When you use the calculator, you will enjoy the following benefits

It is convenient for people who want to do the complicated calculation by the use of the online scientific calculator.  Now you can work wherever you are as far as you can connect to the internet. You are able to use the calculator whenever you feel like it.

Easy

The online calculator may be used easily. There is the manual help with the help function that will guide you if you are not sure about the buttons that you can use in clicking to get to the calculation.

The user friendly interface: the calculator is not complicated and its interface is user friendly. The buttons have been arranged well as it happens with other normal scientific calculators.

The calculator can be used to perform both easy and complex calculation. The example is that you can use it so that you can calculate income tax benefits, property taxes or house loans.  It can be used by students or business people.

If you are not using the quadratic formula calculator, then you can use the quadratic formula which helps to solve quadratic equation and it is among the top five formulas found in math. Even if you should not be memorizing the formulas, this one should be memorized so that you can use it whenever you need it.

Functionality and Description of Math Calculators

A calculator is said to be a small electronic device that performs both involved and mathematical arithmetic operations. It’s also referred to as a machine that makes math operations easy to solve. These tasks are addition, subtraction, multiplication, and division. The advanced math calculators can do square roots, draw functions and can help in calculus. A computer or a smartphone is also known to be a calculator. A calculation calculator contributes to tackling mathematical problems.

Math Calculator
Math Calculator

Types of Math Calculators

Math calculators are found all over the internet and outside in the real world varying regarding cost. It’s crucial to know which math calculator you need to perform a certain job. There are three most common calculators;

  1. Handheld calculators:

Handheld calculators are the most basic calculator found in the world today. It’s simple to handle, pocket-sized, powered by the solar and used for basic mathematics only. The calculators come in attractive colors, designs and are often stylish. Basic calculators contain fewer functions and display results in just a line. The calculators are known as four function calculators since they do perform only addition, subtraction, multiplication and division only. We do have other calculators that can do basic functions such as tax, calculations and discount amounts. Handheld calculators can also copy values between the sub-display and the primary display, or independent actions can take place simultaneously.

  1. Printing calculators:

These calculators were used a long time before computers were created to run all the total numbers over a particular period. They feed off a role of tape to provide a record of the calculations made. They can print in two colors mainly black and red to represent positive and negative values form of identification. They are fast and known to keep up with most experienced Integer cruncher. Printing calculators are large; they are quick, and their display is better than the handheld calculators.

  1. Scientific calculators

They are calculators that offer a broad range of conversions, analysis, statistics and data plotting. The calculators are the most advanced calculators and provide a variety of functions to solve mathematical problems. Most scientific calculators used the VPAM method, a kind of notation for various algebraic functions. The calculator contains quite some math functions that offer mathematicians the ability to tackle complex tasks like fraction calculations, permutations, and combinations. They have some of the features listed below;

  • Dot-matrix display with a high-resolution screen that allows graphs and numbers to be spotted clearly.
  • 2-digit and 10-digit mantissa exponential display
  • A sophisticated memory that is quick and easily recalls previously done calculations
  • Re-execution and editing of formula
  • Editing of data input and back viewing.

Before the creation of math calculators, math was done using pencil, mind, and paper. The four function calculator has by time evolved to be a readily available calculator that meets our needs. They are those powerful calculators that feel the industry and academic needs which do different functions from a core and ordinary calculators. These advanced calculators can be programmed, and some have print out features.

How to find Factors of any Algebraic Equation with the help of Factor Calculator?

Factoring calculator is a simple technique to find out the factors of any number with a real-time value. The algebra is the important and crucial part of the mathematics where most of the students get scared to solve an algebraic equation with higher degree coefficient. Every student has to do various operations like addition, subtraction, multiplication, and division for any equation. Thus, you have an option like either uses Vedic mathematics method or choose factor calculator.

Let us consider an example, how to find out the factors as:

(x + 2) (x – 2)

x² + 5x – 6 = 0

x³ + 4x² + 12x + 12 = 0

These are some examples of an algebraic equation that required huge attention while finding their factors. It is an easy task to find out factors of any numbers but difficult when you are going to find factors of an algebraic equation.

Finding factors for linear equation, let us consider some examples as-

  1. 3x – 6 = 0
  2. 2x + 4x – 24 = 48
  3. 13x / 4 = 39

These are some linear equation whose factors you are finding. It is quite easy to find factors of linear equation. First transfer the number opposite to the equal sign. If there are more than two variables, then try to add them and transfer remaining part to the different side of the equation. You need to eliminate the coefficient term to find the factors of any linear equation. Read the content, to know the method that how to solve an algebraic equation solution-

For first equation:

  • 2x – 5

2x = +5

x=+5/2

  • 3x – 6 = 0

3x = 6

x = 6/3 = 2

For second equation

2x + 4x -24 = 48

6x – 24 = 48

6x = 72

x = 12

Now, the factor is 12

For third equation

13x / 4 = 39

x = 3*4

x = 12

It is very simple to find out factors for a linear equation. On the other hand, you feel difficulties while solving higher degree order of algebra equations. Consider a quadratic equation to find out factors by factoring calculator. Quadratic equation can be solved by the below standard formula as-

math

 

Put the values of a, b, and c in the formula to find out the factors of given algebraic or quadratic equation. For better understanding consider a quadratic equation as

x² + 5x + 6 = 0

Now, put the values of number, coefficient, and coefficient of now, you will get the figure as

math

Therefore, x = -2

By solving above equation, you can get the value for X. The major concern is that the student needs to perform various mathematical operations which are difficult to solve. Thus, you can find factoring calculator to find the factors of given equation. Here you do need to enter a question in the required field then you will get the right solution of any algebraic equation. Whether the equation is linear, quadratic or higher order degree, you can find its factors within seconds. You will get the explained solution or the short answer.

  • Using factoring calculator, you need to perform less mathematical operations.
  • Factoring calculator can easily solve your algebraic equation.
  • With the help of factoring calculator, you can directly put variables and get your desired answer.
  • Use digital algebraic calculator to find out factors

These are some benefits of using the factoring calculator to find out factors of any algebraic equation.

Adding Fractions

A lot of people are terrified when they are required to add fractions. Many even take out a calculator, convert the fractions to decimals and add them together that way. Don’t worry, though; adding fractions is not nearly as difficult as many make it appear. The best thing about knowing how to add fractions is that once you know how to add fractions, you can subtract them from each other just as easily.

Adding Fractions
Adding Fractions

This is very important: The key to adding fractions is to make sure that the denominators of the two fractions you are adding (the numbers on the bottom) are equal. This is not necessary for fraction multiplication, and thus it is a source of confusion for many.

Before you attempt to make the denominators the same, it is advisable to put both fractions in lowest terms (also called simplifying). Now, in order to make the denominators equal, you’re going to want to multiply each denominator by the opposite denominator. Keep track of what number you’re multiplying each denominator by, as you’ll need to multiply the numerator of the fractions by that number as well. Once you’ve done that, you simply add the numerators. In practice, this looks like 3/4+1/7=(7/7)*(3/4)+(4/4)*(1/7)=21/28+4/28=25/28

There are other ways to equalize the denominators, but this is a technique that works in all cases in which you are adding two fractions together. To add more than two fractions, it is easiest to add two together and then add that result to the third (that will keep the denominator “juggling” simple).

A lot of people are terrified when they are required to add fractions. Many even take out a calculator, convert the fractions to decimals and add them together that way. Don’t worry, though; adding fractions is not nearly as difficult as many make it appear. The best thing about knowing how to add fractions is that once you know how to add fractions, you can subtract them from each other just as easily.

This is very important: The key to adding fractions is to make sure that the denominators of the two fractions you are adding (the numbers on the bottom) are equal. This is not necessary for fraction multiplication, and thus it is a source of confusion for many.

Before you attempt to make the denominators the same, it is advisable to put both fractions in lowest terms (also called simplifying). Now, in order to make the denominators equal, you’re going to want to multiply each denominator by the opposite denominator. Keep track of what number you’re multiplying each denominator by, as you’ll need to multiply the numerator of the fractions by that number as well. Once you’ve done that, you simply add the numerators. In practice, this looks like 3/4+1/7=(7/7)*(3/4)+(4/4)*(1/7)=21/28+4/28=25/28

There are other ways to equalize the denominators, but this is a technique that works in all cases in which you are adding two fractions together. To add more than two fractions, it is easiest to add two together and then add that result to the third (that will keep the denominator “juggling” simple).

As mentioned earlier, subtracting fractions is just as easy. All you have to do is equalize the denominators and subtract the second numerator from the first numerator.

How Quadratic Equation Calculator Works

The quadratic equation calculator uses the quadratic formula in order to find the solution for the quadratic equation. The calculator can solve the quadratic equation if you type a simple type of the formula such as A, b, and C and then to hit the solve button.

Some calculator will show how the formula was used, but when you use the graphing calculator, you will solve the quadratic equation even with these that have the imaginary solution.

Quadratic Equation
Quadratic Equation

The calculator to solve the quadratic equation will help you to solve equation through completing the square and by the use of the quadratic formula. The calculator can write down the complete solution step by step.

With the calculators, you will not have to worry that there is something you do not understand. You will be taken to step by step in the learning process.  The algebra worksheet is the best way that you may hone the math skills and to practice if you have a math test.  You will not only learn about a possible solution but also get some tips.

The quadratic equation calculators are here to help you when you get stuck with a problem, and you are not able to figure it out. The calculator can help to solve the equation, and it gives details on how the problem was solved and how the answer was reached.   There are different online calculators online, and they work differently.  Some calculator can solve the problem through factoring, through completion of the square root or answering of the algebra questions.  You may find the graphing calculator, and they plot the equations. The calculators do use the technology, and it allows the plotted graphs to use up to 360 degrees. They provide a well-rounded understanding of the problems.

You can also find the algebra solvers on different websites. They are like the algebra calculator, but they are the software that offers the answers even on the tough equation.  What you will need to do is entering algebra problem, and then the software is going to do what it is left. The great algebra tool may help in providing the tutor whenever the student needs him, and it helps to reduce the costs with the long hours which come with paying the tutor.

If you want to find these calculators, you will only have to enter the name of the calculator you want in Google search. You will get some different calculators, and it is up to you to choose the one you like most.

The calculator helps the students who think that quadratic equations are a nightmare. When the students start to use the calculator and to keep up with their guides, then they will start to solve the problems on their own.

The calculator will put the method into chunks so that the students can learn about them much easily. The quadratic formula can be a mouthful but when it is divided into chunks, it will be manageable. When students see such method, they will realize that they will also use the same methods to other areas of the studies.

What are the Basic and Right Rules for Dividing Fractions?

Fractions have its set of rules for multiplication, division, subtraction and also for addition. Multiplication of fractions is easy, but the division of fractions it little difficult. However, if you know the rule of dividing fractions, you can easily divide two fractions very easily. Fraction is one of the important concepts of the algebra, and you should know the operations on fractions like the multiplication and the division. It is important as you will come across with fractions while studying the algebraic equation and various problems of algebra. Here, you can get informed about the division as well as multiplication of fractions.

Before you study how to divide the fractions, you should know how to multiply fractions. It will help you in the division also. If you do not know how to multiply two fractions, you can’t divide the fractions. The rule of multiplication is very simple. Multiply the denominator of the first fraction with another fraction and just like multiply the numerators of both fractions. So you will get a new fraction after multiplication.

How to divide the fractions?

The basic rule for the division of fractions is simple. Dividing fractions is followed by the reciprocal and multiplication. It’s the single operation in which you have needed to reciprocal a fraction. You can better get it by reading the simple steps of division listed below.

Step 1: first invert the divisor fraction only and use the inverted divisor.

    Step 2: now, rewrite the problem and replace the multiplication sign “x” to the division sign “÷” and also replace the divisor fraction by its reciprocal.

    Step 3: multiply the numbers at the numerator place of both fractions.

    Step 4: multiply the numbers at the denominator place of both fractions.

Step 5: if possible, reduce the fraction obtained by multiplication into its lowest form.

Example:  

Math
Math

Important thing to consider

But keep in mind that you have only to reciprocal only a single fraction. So, do not reciprocal or invert both the fractions which you are using for the division. So, you have only required inverting the divisor fraction only. There is no need to invert the dividend according to the rule of fraction division. In simple words, only invert the second fraction and use the first fraction as it is to solve fraction division problems. It is the most important consideration for dividing fractions correctly.

The same rule will be followed in the problems of dividing a fraction by a whole number. You have to invert the whole number in this case as the whole number is the divisor. So, the whole number will automatically convert into a fraction. You will get a new fraction and then multiply the numerators and denominators.

In this case, convert the whole number into its reciprocal by putting 1 in the numerator and the number at denominator place. So five becomes 1/5, and it is the reciprocal of that number.

Math
Math

Thus, you can easily get the right solution of the dividing fractions problems. You can divide a fraction by another fraction by following the reciprocal and multiplication rule.