Question

How do you factor `6x^2-13x+6`?

Answer 1

`6x^2-13x+6=color(green)((2x-3)(3x-2)`

Explanation:

`6x^2-13x+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 = -13`
After trying out a few numbers we get `N_1 = -9` and `N_2 =-4`
`-9*-4 = 36`, and `-9+(-4)= -13`

`6x^2-13x+6 = 6x^2-9x-4x+6`

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

`(2x-3)` is a common factor to each of the terms

`=color(green)((2x-3)(3x-2)`