Question

How do you factor `6x^2 - 5x - 6`?

Answer 1

`6x^2 - 5x -6`

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 = 6*(-6)= -36`
and,
`N_1 +N_2 = b = -5`

After trying out a few numbers we get `N_1 = -9` and `N_2 =4`
`(-9)*4 = -36`, and `-9+4= -5`

`6x^2 - 5x -6 =6x^2 -9x + 4x -6`

`=3x(2x-3) +2(2x-3 )`

`(2x-3)` is common to both the terms
`color(green)((3x +2)(2x-3)` is the factorised form