Factorisation
Split the middle term instantly.
Core Concepts
Factorisation is the reverse of multiplication. We use the Adyam Adyena (First by First) and Antyam Antyena (Last by Last) principles.
Splitting the Middle Term
For x² + 5x + 6:
Find two numbers that:
1. Multiply to give 6 (Last term).
2. Add to give 5 (Middle term).
Numbers are 2 and 3.
So, (x+2)(x+3).
Difference of Squares
a² - b² = (a+b)(a-b)
Example: x² - 9
x² - 3² = (x+3)(x-3).
Solved Examples
Example 1: x² + 7x + 12
Question: Factorise.
• Find numbers that multiply to 12 and add to 7.
• 3 × 4 = 12.
• 3 + 4 = 7.
• Answer: (x+3)(x+4).
Example 2: x² - 5x + 6
Question: Factorise.
• Multiply to 6, Add to -5.
• -2 × -3 = 6.
• -2 + -3 = -5.
• Answer: (x-2)(x-3).
Example 3: x² - 16
Question: Factorise.
• This is x² - 4².
• Use difference of squares formula.
• Answer: (x+4)(x-4).
Example 4: x² + 6x + 9
Question: Factorise.
• Multiply to 9, Add to 6.
• 3 × 3 = 9, 3 + 3 = 6.
• It's (x+3)(x+3).
• Answer: (x+3)².
