# How to factor?

Kristina Firsova
March 25, 2013

Mathematics is an interesting science, but sometimes it is quite complicated. Formulas and rules, as well as the multiplication table will help in solving complex problems. In addition, they will provide an opportunity to navigate on the question of how to factor out prime numbers and polynomials.

## How to decompose a number into factors

In order to figure out the factors of a number, you need to find its smallest divisor. It should be simple and whole. If you are recording actions, you need to draw a vertical line, dividing the sheet into two columns. Record the original number in the upper left. Now think about what is the minimum number you can divide this in order to get a whole number without remainder. Write it on the left, and the result of the division is on the right. This should be done until the last digit in the column is one. Remember that you can not divide the number by one. You need to choose from two and higher. For example, you need to find the factors of the number 468. The minimum divisor is 2. Write on the left 2, on the right the division result is 234. Find the divisor of this number. This is also 2.It is necessary to divide 234 by 2. It turns out 117. Write the result in the columns. Divide 117. We cannot divide 2, because it is not an integer. Try 3. This number is suitable, write it and the result of the division. The answer is 39. At what minimum number can you divide 39? This is also 3. The answer is 13. This number can be divided only by itself - by 13. It turns out 1. So, you derived all the factors of the number 468. Write them down below.

## How to decompose a number into prime factors

In order to factor out a number, you need to know the multiplication table. The fact is that if your number is small, its prime factors are easy to find. For example, you want to calculate the prime factors of the number 10. You need to determine what the smallest number you can divide this number is 2. We take all the numbers, except one. As a result, we obtain: 2x5 = 10. This means that the numbers 2 and 5, since they are simple, are multipliers of 10.

## How to decompose a polynomial into factors

In principle, as with primes, there is nothing complicated. The actions are the same, only the number has several members. Before expanding the polynomial into factors, you need to take the common factor out of the bracket. For example: 16 in a cube - 24 in a square.Spread each number into the smallest dividers. What happens: 4y squared * 4y - 4y squared * 6 = 4y squared (4y - 6). This will be the answer.

You can apply a method called "grouping." The principle of operation is the same. You just need to group the polynomials, put the total out of the bracket. Then you need to find a common factor for each bracket. We also take it out. The numbers in brackets will be multipliers of polynomials. Another way - the method of "abbreviated multiplication." It is necessary for each polynomial to find out the factors and put them in brackets. You need to do this procedure until you reach the unit.