In the quadratic factorisation we perform splitting of the middle term. which is term is that the sum of two factors and the product equal to the last term.
Example:
Factorize .
To form the factor: where (\(a = 6\), \(b = 19\) and \(c = 10\)).
Step 1: Find the product of the first and last term \((a × c)\).
.
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).
and .
Step 3: Write the middle term using the sum of the \(2\) new factors, including the correct signs.
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.
Step 5: Factor out the common factors from the term.
The factors of is .