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# Factoring Algebra

Math factoring is very much useful in almost all the fields of mathematics. In factoring Algebra, factors are any algebraic expression which divides another algebraic expression where the remainder is zero. Similarly in case of Numbers we use numbers instead of algebraic expressions.For instance: 4 and 2 are the factors of 8 which means that both the numbers divides 8 completely as 8 ÷ 2 = 4 and 8 ÷ 4 = 2.

We can also define factors as the numbers which we multiply so that we can get other number. For example factors of 12 are 3 and 4, because 3*4 = 12. Some numbers may have many factors. Example is 16 can be factored as 1*16, 2*8, or 4*4.
The number which can only be factorized as 1 and itself then that number is called prime number. For example 2, 3, 5, 7, 11, 13 . . . . are the Prime Numbers. The number 1 is always ignored in case of Factorization because it comes always in almost everything and it do not considered as a prime number.

The factorization of prime numbers does not include 1. It includes all the copies of each and every prime factor. For example: Prime factorization of 8 = 2*2*2 that is not only 2. Here 2 is the only factor of 8 but it is not sufficient means we need three copies of 2 so if we multiply 2 by itself 3 times we get back 8; therefore the prime factorization of 8 includes 3 copies of 2.
Again if we look at the prime factorization it will only consider the prime factors not the products of those factors. For example: 2*2 is 4 and 4 is a divisor of 8 but 4 is not considered as a prime factor of 8. Because 8 is not equal to 2*2*2*4.
Suppose in factoring Math the task is to get the prime factorization of 24. Now if we only collect all the divisors of 24 as 1, 2, 3, 4, 6, 8, 12, and 24 and we multiply all the divisors of 24 as 1*2*3*4*6*8*12*24 will result in 331776 which are not 24 so it is not the right way. So we use prime factorization, either the problem needs it or not to avoid such over duplication or multiplication. So for this we can find the prime factor of 24 by dividing 24 by the smallest prime number which is 2 i.e. 24 / 2 = 12. Now again divide the result 12 by the smallest prime number 2 as 12 / 2 = 6; again divide 6 by 2 as 6 / 2 = 3 and here we get a prime number that is 3 so we do not need to further divide this because the prime numbers has factors 1 and itself; so we are done. So the factors of 24 are 2, 2, 2 and 3.
Find the prime factor of 1008
Solution:
1002 ÷ 2 = 504
504 ÷ 2 = 252
252 ÷ 2 = 126
126 ÷ 2 = 61
So it has solution 1002 = (504) (252) (126) (61).

## GCF and Prime Factorization

To find the factors of any number means to write the number in form of its multiples. If the factors of the  number are all prime Numbers, then we say that the factors are prime factors. For this we go on breaking the number in form of its multiples until we get all its factors as the Prime Numbers. E.g.: Prime factors of 20 = 2 * 5  * 2 * 1. Here if we write...Read More

Any equation which can be written in the form: ax2 + bx + c = 0 where we have a, b, and c as the real Numbers and value of ‘a’ is not equal to zero, than it is called as Quadratic Equation. Here we will learn how to solve quadratic equation. Let us consider a real number ‘α’ (alpha) which is the root of the quadratic equation ax2 + bx + c = 0, a≠0, if aα2+ bα...Read More

## Factor Trinomials

It is just reverse process of multiplying. Factoring Trinomials is always in the form of x2 + bx + c. It is just opposite of Foil Method i.e. the process which is used to multiply two binomial values. Distributive property explains how to multiply a single value such as 8 by a binomial such as (6 + 8x) which is represented as 8 (6 + 8x).
If there is an expression w...Read More

## Factoring GCF

Word gcf means to find the greatest common factor. Factoring gcf, also means to find the highest common factor. When we find the factors of any number it means that we need to find the Numbers which are divisible by the given number. If we write that 3 is the factor of 12, it means that 12 is completely divisible by 3 and does not leave any remainder. Factoring by gcf, can...Read More

## Factoring Difference of Square

When an algebraic expression can be written in the form of the product of two or more expressions, then each of these expressions is called as the factor of the given expression. We find the factors of the algebraic expression with the aim to simplify the expression and it will help us to make the calculations easier and fast when the variables in the expr...Read More

## Factoring Perfect Square Trinomials

Perfect Square trinomial is a trinomial which when factored gives two identical factors or we can say that the factors are same.
For example we have an equation p2 + 8p + 16; then we can write it as. (p + 4) (p + 4) or we can write it as (p + 4)2.
For factoring a perfect square trinomial we need to follow some steps: