# How do you factor the expression 6x^2 - 21x - 9?

Apr 23, 2016

$\left(3 x - 9\right) \left(2 x - 1\right)$ or $\left(2 x - 1\right) \left(3 x - 9\right)$

#### Explanation:

When factorizing, we have to make sure that we get the middle number when a quadratic equation is factorized. In order to check whether we have gotten it or not, do the cross addition (green in the picture).

Please note, and do NOT confuse that when you factorize the quadratic equation you factorize parallel numbers on opposite sides (black arrow in the picture).

Apr 23, 2016

$\text{ } \left(2 x - 1\right) \left(3 x - 9\right)$

#### Explanation:

Some times they are easy to spot, sometimes they take a lot more work.

It is a matter of splitting up the 'expression' so that common factors become evident. After a bit of experimentation I came up with the following:

Given:$\text{ } 6 {x}^{2} - 21 x - 9$

Write as:$\text{ } 6 {x}^{2} - 3 x - 18 x - 9$

Now group them

$\text{ } \left(6 {x}^{2} - 3 x\right) - \left(18 x + 9\right)$

Factor out common values within each bracket giving

$\text{ } 3 x \left(2 x - 1\right) - 9 \left(2 x - 1\right)$

Factor out the $\left(2 x - 1\right)$ giving

$\text{ } \left(2 x - 1\right) \left(3 x - 9\right)$