A factor: The complete set of whole numbers called factors. When you will multiply one number by the neighbor number of the set, you would get the factoring number. Such as the number 3 has two factors 1 and 3 and the number 8 has four factors 1, 2, 4, and 8. Which factor contains negative numbers called integer factors. In that case 3 has four factors: -3,-1, 1, and 3. 8 has 8 factors: – 1, -2, – 4, -8, 1, 2, 4, and 8. 1, 2, 3, 4, 5 are the natural numbers. There is not any fraction of the natural number. From 0 to infinity all whole numbers are natural numbers. Integers are also natural numbers with including negative counterparts. It is not so difficult how to factor numbers with the natural numbers. You can find at least two factors in any number.
How to find factor from the natural number:
If you want to find a factor of any number, then you will start to divide it. Without the number 9, you can continue dividing numbers until it reached into 2. When you do not find any rest that means both are divisor and the remaining common quotient are its factors. Now, look at the number of 9. It is divided by 3 and 1 but not divided by two. The factors of 9 are 1, 3, and 9.
For the integer set, you need to add negative equal numbers to your results. Such as 9 have the integers set is -9, -3, -1, 1, 3, and 9. There is only one integer that has infinite factors. This integer is zero. One is the only number which has zero as a factor.
Factoring in an expression:
An algebraic expression carries some number which called coefficient, variables, and constant.
In the expression x2 + 4x + 8, where 1 is the coefficient of x2. 4 is the coefficient of x, and the constant is 8. A constant is not multiplied by a variable. When the power of a variable is 0 then it will be, x0=1.
For factoring an expression, we need to collect the Greatest Common Factor (GCF). In the expression collect the factors of every component.
Take this equation x2 + 4x + 8, it has factors look bellow
4x- 1, 2, 4
8- 1, 2, 4, 8
In that equation, we find only the common factor is 1. It has no coefficient greater than one. Look another expression that is
2x3+ 16 x2 + 6x. Its factors are
X2– 1, 4, 2, 8, 16
x- 1, 2, 3, 6
Here we find the common factors are 1, and 2. Now multiply two with the variable x we find 2x. Divide every component in the expression by 2x.
2x3/2x = x2
16 x2/2x= 8x
6x/2x = 3
Now we find the GCF how to factor out. That is
2x(x2 + 8x + 3).
How to find factors of a binomial expression:
Which expression has two terms of a variable is calling binomials. 2x2– 6x is a binomial expression. From this equation, we look the GCF factors are
2x(x-3). (X-3) has no any factor.