Factoring Polynomials – How to Factor Polynomials?

Factoring is an important term in mathematics which let you to fi9nd t6he products of a polynomial. Well, you will need to practice this as it is easy, but without practice, one will not be able to understand its pattern.  For factoring polynomials, one should be excellent at factoring numbers plus must have the basic knowledge of algebra. So, today, we are looking for the methods for factorizing these polynomials and convert it into a binomial. 

Steps to factories polynomials

Yes, you need to learn steps as one should know as which to do at first to factories it. The most significant term included in it is Greatest Common factor which is an abbreviation of GCF. 

·         In the first step, you need to find out the greatest common factor.  If you don’t know what GCF is, then let me tell you that it is the biggest expression that will be common in all the terms. In other words, while solving polynomials, one has to find a number which must be a common factor or number in all the terms from which it is obtained.

·         In case you will get a trinomial in which the equation contains three terms and for4 solving that terms one can take help of a FOIL method.

·         In case, it is a binomial one should look for the sum of cubes or different of squares. And after you factories all the polynomials then one has to use zero as a product property to find the answers.

 Now, let’s factorize polynomials with an example. Let’s solve equation 

So, let’s start answering it:  

Now, in the next step, consider 10 and factorize this number. After you finish factorizing it, you will get 5 and two from it.

Now, 

Well, we write (5x) and (-3x) to factorize these polynomials. Besides his, always make sure that you will put right sign before the number as a single wrong sign will give you the right answer. Besides this, you need to know all the rules of signs.

Now, you have to take common x from the equation like:  

Now, after this whole calculation, you have to take zero products for finding out the value x. Now,

x+5=0 which will give you x = -5 and (x-2) will give you, x=2.

So, this is the entire solution of the trinomial equation. Well, there are still various things which you should consider while factoring polynomial:

·         Make sure that you learn about the signs at first because using proper sign is an essential part of the solution.

·         Remember this common rule of signs: 

·         Besides this, arrange the middle terms in a way that its sum will be equal to the last term and its product will be equal to the middle value of the equation.

Factoring polynomial is full of fun, and when you get used to it, and then you will love to solve such problems. Math is just full of fun when you start understating its concepts.

Know a Simple Method for Adding Fractions with Same Denominators and Different Denominators

You may have come across with fractions often since you are studying the factions. They come in the formulas, algebraic equations, and some practical problems. Algebraic equations contain fractions, so it is an important topic to solve the equations of algebra. You should study about adding fractions that contain algebraic expressions.  However, numbers are included in the fractions of arithmetic. You should know all the operations on fractions as they are useful for various problems. You must be capable of solving addition, subtraction, division and multiplication of different fractions. Here, you will study how to add two different fractions that are containing only numbers by an easy method.

Adding fractions 

Types of fractions

Firstly, you should be aware of the different types of fractions. There are usually two kinds of fractions used that are like or same fractions and unlike fractions for addition. The like fractions are the fractions that have the same number at the denominator place like 2/3 and 4/3. Whereas, the, unlike fractions, has different numbers at the denominators place like 2/3 and 4/11. You should able for adding fractions of both like and unlike fractions.

To add the like fractions

To add two different fractions having same denominators is simple. You have to add only the numbers at the numerators of both the like fraction. After adding the numerators, check whether it can be simplified further or not. If the fraction can be simplified that is it can be reduced, you should correctly convert it into lowest form. It is explained in the example below.

So, as the both the denominators are same, you can add it as, 

It can be reduced further as both 4 and 8 are divisible by a common number that is 4. Thus, the correct answer to this problem will be,  

To add the unlike fractions

To add two unlike fractions is little tricky, as the denominators are not same. In this case, you have to make the denominators of the fraction same. So convert the fractions so that they have the same denominator and then simply add them. For adding fractions easily, you must ensure sure that both the bottom numbers that is denominators are same.

    Firstly, convert the unlike fractions to like fractions by making both the denominators same.

    Then, you have to add only the numerators of both the fractions, as the denominators are made same.

    Then, if the fraction obtained after addition can be simply further, you must convert it into lowest or reduced form correctly. it will be your final answer that would be a fraction.

Consider this problem to understand it better, and you can easily add the fractions.

Firstly, you have to make both the denominators same as they are different that are 3 and 6. If we multiply both the numerator and denominator of the first fraction by 1/3 by 2, it can be converted to 2/6. So, you can add this new fraction with the second fraction 5/6 that gives the answer as 7/6.

So, you have studied to add the arithmetic fractions. Adding fractions in the way to add two algebraic fractions is also simple for you.