Factorization by common factors

Suppose we want to factorise,

  2x + 4

Find, we find common factors individually

  2x = 2 × x

  4 = 2 × 2

Since 2 is common, we take that out

So,

  2x + 4 = 2 × x + 2 × 2

   = 2 (x + 2)

So,

  2x + 4 = 2 × (x + 2)

Let’s take another example

2 x y + 2y

Finding factors

  2xy = 2 × x × y

  2y = 2 × y

So, 2 & y are the common factors.

So,

   2xy + 2y = 2 × x × y + 2 × y

 = 2 × y (x + 1)

 = 2y (x + 1)

So,

  2xy + 2y = 2y (x + 1)

5x ² y + 10x

Finding factors

     5x ² y = 5 × x ² × y

             = 5 × x × x × y

      10x = 10 × x

             = 2 × 5 × x

So,

      5x ² y + 10x = 5 × x × x × y + 2 × 5 × x

   = 5 × x (x × y + 2)

   = 5x (xy + 2)