Method of Common Factors
Factorise 2x + 4 (Write each term as a product of irreducible factors)
We can write 2x =
and 4 =
Therefore we get,
2x + 4 = (2 x) + (2×2)
We notice that the factor 2 is common to both the terms. Using the
2(x + 2) = (2×x) + (2×2) (for the above case)
Therefore, we can write:
2x + 4 = 2×(x + 2) = 2(x + 2)
Thus, the expression 2x + 4 is equal to 2 (x + 2). In this form we can easily see the factors for the expression: 2 and (x + 2). These factors as we know, are
Factorise 5xy + 10x and find the common factor between the two terms
- The common factor :
- Factorised form =
- Taking out the common factor
- Which gives us the above answer
Therefore, 5xy + 10x = 5 x (y + 2) which is the factorised form.
Example 1: Factorise the following expressions:
- The common factor(s) product :
- Thus, factorised form =
- Taking out the common factor
- Which gives us the above answer
Example 2: Factorise
- The common factor(s) product :
- Thus, factorised form =
- Taking out the common factor
- Which gives us the above answer
TRY THESE
Factorise: (i)
- The common factor(s) product :
- Thus, factorised form =
- Taking out the common factor
- Which gives us the above answer
(ii)
- The common factor(s) product :
- Thus, factorised form =
- Taking out the common factor
- Which gives us the above answer
(iii) 12x + 36