Factorization of Quadratic Expressions II

Factorization of Quadratic Equation by Splitting the Middle Term:

In order to factorise a quadratic expression of the form ax² + bx + c, where \( \scriptsize a \neq 1 \) 

Consider the quadratic equation ax² + bx + c = 0

Step 1: Multiply the coefficient of x² and the constant term c

i.e. a × c = ac

Step 2: Now, find two numbers such that their product is equal to ac and their sum is equal to b .

Product: (number 1)(number 2) = ac
Sum: (number 1) + (number 2) = b

Step 3: Split the middle term : Split the middle term using these two numbers

x² + (number 1)x + (number 2)x + c = 0

Step 4: Factorize by grouping

Step 5: Factor out the common bracket