How to factorize

How to factorize

We display an integer and a polynomial on multipliers. We remember a school technique of division in a column.


1. Any integer is possible to spread out onsimple multipliersfor .Dlya of it it is necessary to divide consistently it into numbers, since 2. And it can turn out so that some numbers will enter decomposition more than once. That is, having divided number into 2, you do not hurry to pass to the three, once again try to divide it into two. And here we will be helped by criteria for divisibility: on 2 even numbers share, is divided into the 3rd if the sum of the figures entering it is divided into three, on 5 the numbers terminating on 0 and 5 share. It is the best of all to divide in a column. Since the left figure of number (or two left figures) consistently you divide number into the corresponding factor, write down result in private. Further you multiply intermediate private by a divider and you subtract from the allocated part of a dividend. If the number is divided into its estimated simple multiplier, then in the rest zero has to turn out.

2. The polynomial can also be factorized. Here various approaches are possible: it is possible to try to group composed, it is possible to use the known formulas of the reduced multiplication (the difference of squares, a square a sum/difference, a sum/difference cube, the difference of cubes). It is also possible to use a trial and error method: if the number which is picked up by you approached as the decision, then it is possible to divide an initial polynomial into expression (x-(this found number)). For example, column. Polynomials it will be divided totally, and its degree will go down on unit. It is necessary to remember that the polynomial of degree of P has no more than P various roots, but roots can coincide therefore try to substitute the number found above in the simplified polynomial - quite perhaps that division by a column can be repeated once again. The received result as performing expressions of a look (x - (root 1)) * registers (x - (root 2))... etc.

Author: «MirrorInfo» Dream Team