Question

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

Answer 1

`(9x+2)(x-3)`

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 xx 3 = 27` which is near to `25`.)

`color(white)(.......)9" "2 " "rArr1xx2 = 2`
`color(white)(.......)1" "3 " "rArr9xx3 = 27 " " 27-2 = 25`

We have the correct factors, now consider the signs:

`color(white)(.....)9" "+2 " "rArr1xx+2 = +2`
`color(white)(.....)1" "-3 " "rArr9xx-3 = -27 " " -27+2 = -25`

`rArr(9x+2)(x-3)`