Factors of Algebraic Expressions
We are aware that in algebraic expressions, terms are a product of its factors. For example: in 5xy + 3x
5xy =
Is there an important observation here? We can see that the factors 5, x and y of 5xy cannot be further be expressed as products of smaller factors. In other words, we can say that 5, x and y are ‘prime’ factors of 5xy.
In the case of algebraic expressions, we use the word ‘irreducible’ in place of ‘prime’. Thus,
5 × x × y is the irreducible form of 5xy.
Is 5 × (xy) an irreducible form of 5xy ?
5 × (xy) is not an irreducible form of 5xy as the factor 'xy' can be further expressed as a product of x and y i.e. xy = x × y.
Note: 1 is a factor of any number.
Therefore, when we write a number as a product of factors, we do not write 1 as a factor (unless it is required).
Similarly, for say, '5xy'- 1 is again a factor. Even here, we do not show 1 as a separate factor.
Consider the expression 3x(x + 2). It can be written as a product of factors :
3x(x + 2) =
The factors 3, x and (x +2) are irreducible factors of the expression- 3x (x + 2).
Similarly, for the expression- 10x (x + 2) (y + 3) can be expressed in its irreducible factor form as:
10x (x + 2) (y + 3) =