Question

How do you factor `4x^2 + 24x + 11`?

Answer 1

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:
`N_1*N_2 = a*c = 4*11 = 44`
AND
`N_1 +N_2 = b = 24`
After trying out a few numbers we get `N_1 = 2` and `N_2 =22`
`2*22 = 44`, and `2+22= 24`

`4x^2 + 24x + 11 = 4x^2 + 2x + 22x + 11`

`= 2x(2x+1) + 11(2x+1)`

`(2x+1)` is a common factor to each of the terms

`=color(green)((2x+1)(2x+11)`