How to use a Factoring Calculator

What is a factoring method in mathematical aspects?

First, it is important for us to understand what a “factoring” means in mathematical point of view. It means that two numbers have to multiply to equal constant term “c” and yet again sum up to “b” the coefficient on the x term. This method is used to solve quadratic equations that are factor able. So, the factoring calculator tries to solve the equation of it as long as the right values of the coefficients have been fed to that calculator.

Normally, the quadratic equation takes the form of  whereby the values of a, b and c are known while that of x has to be solved or obtained from the equation after it has been solved. In other words, it is safe to say that a, b and c are the numerical coefficients of the given quadratic equations.

To understand the factoring formula better, it is best to illustrate it using an example.

Solving quadratic equations using factoring method

We can take an equation like  and have been told to factor it.

First, we have to find the factors of 6 that add up to 5. But because we can write 6 as the product of 2 and 3, and the two also add up to 5, i.e. 2+3=5. Then, I will have to use 2 and 3 instead of the initial 6.

The above polynomial can be simplified further into the form of (x + m) and (x + n)

Therefore, it is all right to rewrite is this way (x + 2) (x +3).

= (x + 2) (x +3). You can leave it there or continue to get the values of x, which will be

X = – 2 and x =-3 However, this really won’t change anything. So you can leave it at the (x + 2) (x +3) point.

We can take a look at one more example for you to understand it clearly.

Factor,

The best way to approach such the problem is to apply the differences of squares rule which is

=(x + y) (x – y)

Therefore, = ((x – 2)-3) ((x – 2) +3). Simplifying it further will land us on these solutions:

(x – 5)(x + 1)

These two examples have been clearly explained. You can look for many other examples online or on books. There is this website that will save you a lot of time since it has many examples that have been explained step wise. The site is www.quickmath.com. You can visit the page and look for the factoring page within the home page. When you click on us, you will be redirected to a web page that contains the information I am talking about.  You can also raise the alarm if you think the answer they gave is not correct. You will have to send them an email and clearly, tell them what you think is the right answer, and I am sure they will update it immediately.

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Algebra and its Own World

Mathematics is a very big subject and is divided into so many branches like geometry, algebra, quadratic equations, coordinate geometry, calculus and so on. Mathematics enters in all fields of science, and it is essential for the development of science and technology. It is the basis for proving any new scientific theory or making any new discovery.

Quadratic Equation Calculator
Quadratic Equation Calculator

Algebra including quadratic equations can be essentially considered as doing arithmetic operations with non-numeric mathematical entities or objects. This is a very powerful structure because it allows us to proof properties that are true no matter what are the numbers involved. The non-numeric entities can be unknown, and we are required to find them, or they can be unspecified. We have an equation, and we can plug in different values to get different results. Therefore, algebra is used to express the relationship between entities. When we deal with algebra, we mainly deal with expressions and equations. Equations describe the equity relationship between entities and an expression describes a phrase that contains variables, numbers and arithmetic operators. As algebra and quadratic equation calculator developed, the non-numeric entities were extended to accommodate more complex structure like vectors, matrices, and polynomials. It is now accommodating more complex and abstract new structures. This is what makes algebra useful in modelling mathematical and scientific problems that cannot be modelled in any other way.

Algebra took a very long evolution period before it became like the way we know it today. Its roots extend to the ancient Egyptian era and even before that. Algebra started at the time of the ancient Babylonians. They created advanced algorithms to solve certain problems. These algorithms are used today to solve quadratic equations and linear equations. The Egyptians of the same era used to model algebraic problems in terms of geometry and solve them geometrically. So, they considered algebra as an application of geometry. The ancient Greek mathematicians and ancient Chinese mathematicians followed the same example as the Egyptians. The Egyptians developed geometric methods to solve algebraic problems. The Greeks even developed the Egyptian algorithms further to solve more general problems.

All this influenced Muhammad ibn Musa al-Khwarizmi the Arab Islamic scientist who created afterward much of the algebraic method that we know today. The word algebra is an Arabic word and was created after he established algebra as an independent mathematical discipline other than geometry and arithmetic. He established algebra in his book the Compendious Book on Calculation by Completion and Balance.

The classical algebraic discipline did not start before the end of the sixteenth century. In the year 1637, the modern algebraic notion was introduced. Then the solution of quadratic and cubic equations was introduced. Then matrices and determinants were used to solve systems of simultaneous equations. Many other new algebraic concepts were introduced later.

Today we are fortunate that we have many innovative quadratic equation calculator and tools that incorporate all these algebraic ideas into a program that allow us to model real life problems just by pressing buttons and in seconds. We can use the outcome of all these algebraic findings from ancient Egyptians till today using these calculators.

Positive Signs of Factoring Calculator

Factoring is a common function in Mathematics. Especially when dealing with algebra, factoring is so common. Such expressions can be factored either manually or by using more evolved tools like a calculator. These include both the traditional and advanced calculators. The factoring calculator, an enhanced tool for sorting out different operations, helps you reduce lengthy expressions into their shorter and more comprehensible components.

What should you expect?

While executing the factoring command, the system prompts the calculator to carry out various mathematical processes. This includes eliminating common factors, factoring in pairs and factoring of quadratic trinomials. The factoring process also includes finding differences of two or more squares and getting differences of two cubes.

In most cases, people assume factoring to involve only whole numbers and simple algebraic equations. With the factoring calculator, you realise that you can solve much more than the usual expressions. The advanced options of factoring calculator give the option of factoring trigonometric functions. As such, you can be able to work with the tangents and cosines and simplify them further using the factoring calculator. Also, you can also use this calculator to factor over the fields of Gaussian integers. This is quite interesting. You can also extend the field over which you carry out the factoring using this calculator. This provides you with an ideal opportunity of making the most out of such calculators.

Easier way to solve quadratics

Most simple factorization problems involve quadratic equations. These type of equations can be handled with or without the use of factoring calculators. Just for purposes of refreshing the brain, quadratics are expressions that take the general formula ax^2 +bx + c where a, b and c and real numbers that are represented by letters. For factoring easy quadratic equations, you need to find two numbers that will easily multiply to have c the product and similarly add up to find b as the sum. These equations are easily computed using these calculators. Alternatively, you can still sort them out manually and still find your answer the easier way.

It is worth noting that not all quadratic equations will always end up in a similar way. Some of them need advanced factoring technique. In such cases, the factoring calculators become handy.

Making the choicest decision

When choosing the factoring calculator to use for your operations, you need to put into consideration several aspects. For one, you need to analyse the efficiency and efficacy of the calculator. If it is a physical calculator, how easy is it to access the factoring functions? Does it require advanced knowledge to use these functions? You will need to find this out. For the case of online calculators, you will need to be keen on other functions rather than the factoring options. Is the tool reliable enough when it comes to handling larger expressions? Can it be relied upon to provide credible answers? What are the previous users saying about it? Unless you put all these into consideration, you might end up getting disappointed with your choice of factoring calculator.