# Automatic Factoring

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Factoring is a very important and most commonly used method in Algebra to simplify any given expression or
equation. In the method of factoring, a constant or a variable which is common in all the given terms of the
expression or equation is pulled out as a common factor. This simplifies the given expression and hence it is
called automatic factoring.

Example 1: Factor the given algebraic expression: 2x3 + 6x – 10x4.

Given algebraic expression: 2x3 + 6x – 10x4

In the above given expression, the three terms consist numbers such as 2, 6, 10.

These three numbers are multiples of ‘2’; hence ‘2’ is a common factor for all the three terms.

Similarly, ‘x’ is a common factor for the three terms in the given expression!

Hence we get: 2x(x2 + 3 – 5x3)

So the factored form of the given expression,2x3 + 6x – 10x4 = 2x(x2 + 3 – 5x3)

Example 2: Factor the given algebraic expression: 5y5 + 10y4 – 5y3 + 15y2

Given algebraic expression: 5y5 + 10y2 – 5y3 + 15y2

In the above given expression, the four terms consist numbers such as 5, 10, 5, 15.

These four numbers are multiples of ‘5’; hence ‘5’ is a common factor for all the four terms.

Similarly, ‘y2’ is a common factor for the four terms in the given expression!

Hence we get: 5y2 (y3 + 2y2 – y + 3)

So the factored form of the given expression is:

5y5 + 10y4 – 5y3 + 15y2 = 5y2(y3 + 2y2 – y + 3)