Factoring Algebraic Expressions
Similarly, we can factorise an algebraic expression and express it as a product of factors. These factors may be numbers, algebraic expressions or variables.
Factoring is the process of writing a polynomial as the product of two or more polynomials.
Example: Factorise 3x + 6
Write each term as a product of irreducible factors:
3x = 3 × x
6 = 2 × 3
3x + 6 = (3 × x) + (2 × 3)
The above two terms have 3 as the common factor.
By distributive property, 3 × (x + 2) = (3 × x) + (2 × 3)
So, 3x + 6 = 3(x + 2), where 3 and (x + 2) are the factors of 3x + 6, and these factors are cannot be reduced further.
Example: Factorise 10xy + 20x
10xy = 2 × 5 × x × y
20x = 2 × 2 × 5 × x
10xy + 20x = (2 × 5 × x × y) + (2 × 2 × 5 × x)
The above two terms have 2 × 5 × x = 10x as the common factor.
By distributive property, 10x × (y + 2) = (2 × 5 × x × y) + (2 × 2 × 5 × x)
So, 10xy + 20x = 10x(y + 2), where 10x and (y + 2) are the factors of 10xy + 20x, and these factors cannot be reduced further.
- Factorise 7xy + 49x
- Factorise 12x + 36
- Factorise mn + 10m
- Factorise 24a + 30
- Factorise 11x + 121xy
- 7x(y + 7)
- 12(x + 3)
- m(n + 10)
- 6(4a + 5)
- 11x(1 + 11y)
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