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

1 Answer
EZ as pi
Aug 10, 2016

#(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)#

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