Theory:

In the quadratic factorisation we perform splitting of the middle term. which is x term is that the sum of two factors and the product equal to the last term.
Example:
Factorize 6x2 + 19x + 10.

To form the factor: ax2 + bx + c where (\(a = 6\), \(b = 19\) and \(c = 10\)).
 
Step 1: Find the product of the first and last term \((a × c)\).
 
6× 10 = 60.

Step 2: Find the factors of \(60\) using the middle term in such a way that the addition or subtraction of that factors \((19x)\) (Splitting of the middle term).
 
15×4 = 60 and 15 + 4 = 19.

Step 3: Write the middle term using the sum of the \(2\) new factors, including the correct signs.
 
6x2 + 15x + 4x + 10

Step 4: Group the terms to make pairs using the first two terms and also the last two terms. Factor each pair by finding common factors.
 
3x ( 2x + 5)+ 2(2x + 5)
Step 5: Factor out the common factors from the term.
 
(3x + 2) ( 2x + 5)
 
The factors of 6x2 + 19x + 10 is (3x + 2) ( 2x + 5).