How to factorize?

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

How to factor a number

In order to find out the multipliers of a number,find its smallest divisor. It must be simple and complete. If you record actions, you need to draw a vertical line, dividing the sheet into two columns. Record the source number on the upper left. Now think about what a minimum number you can divide a given so that you get a whole without a remainder of a number. Write it on the left, and the result of division is on the right. So it is necessary to do, while the last digit in the column does not remain a unit. Remember that you can not divide a number by one. You need to choose from the two and above. For example, you need to find the multipliers of the number 468. The minimum divisor is 2. Write on the left 2, on the right the result of the division is 234. Find the divisor of this number. This is also 2. You need to divide 234 by 2. It turns out 117. Write the result in the columns. Divide 117. We can not divide by 2, because it is not an integer. Try 3. This number is suitable, write it down and the result of division. The answer is 39. What is the minimum number, 39? This is also 3. The answer is 13. This number can be divided only into yourself - by 13. It turns out 1. So you deduced all the multipliers of number 468. Write them down below.

How to factor a number into prime factors

In order to decompose into prime factorsnumber, you need to know the multiplication table. The fact is that if your number is small, its simple multipliers can be found easily. For example, you want to calculate simple multipliers of 10. You need to determine which smallest number you can divide a given number by 2. Take all numbers except one. As a result, we get: 2x5 = 10. This means that the numbers 2 and 5, since they are simple, are multipliers 10.

How to factorize a polynomial

In principle, as with primes, nothingthere is no complicated one. The actions are the same, only the number has several members. Before expanding the polynomial into multipliers, it is necessary to take the common factor for the bracket. For example: 16у in a cube - 24у in a square. Divide each number into the smallest divisors. What happens: 4y in the square * 4y - 4y in the square * 6 = 4y in the square (4y - 6). This will be the answer.

You can apply a method called"Grouping". The principle of operation is the same. It is just necessary to group the polynomials, to make the general for the bracket. Then we need to find a common factor for each bracket. We also bear it. The numbers in parentheses will be multipliers of polynomials. Another way - the method of "reduced multiplication." It is necessary for each polynomial to find out the factors and put them in brackets. Do this procedure until you reach one.