How do you factor 9x^2- 25x -6?

Aug 10, 2016

$\left(9 x + 2\right) \left(x - 3\right)$

Explanation:

We need to find factors of 9 and 6 which subtract to give 25.
The signs in the brackets need to be different, with more negatives.

Use factors of 9 and 6 and subtract the cross products to get 25.
(It helps to notice that $9 \times 3 = 27$ which is near to $25$.)

$\textcolor{w h i t e}{\ldots \ldots .} 9 \text{ "2 " } \Rightarrow 1 \times 2 = 2$
$\textcolor{w h i t e}{\ldots \ldots .} 1 \text{ "3 " "rArr9xx3 = 27 " } 27 - 2 = 25$

We have the correct factors, now consider the signs:

$\textcolor{w h i t e}{\ldots . .} 9 \text{ "+2 " } \Rightarrow 1 \times + 2 = + 2$
$\textcolor{w h i t e}{\ldots . .} 1 \text{ "-3 " "rArr9xx-3 = -27 " } - 27 + 2 = - 25$

$\Rightarrow \left(9 x + 2\right) \left(x - 3\right)$