How do you factor the expression #30x^2+x-1#?

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Answer 1 · 2016-03-01T22:18:33

#(5x+1)(6x-1)#

The only possible construct to give -1 as the constant has to be of form #(?x-1)(?x+1)#

We need two factors of 30 that have a difference of 1 to give #1x#
#5xx6# looks promising so lets try it.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#(5x-1)(6x+1) = 30x^2 +5x-6x-1 = 30x^2-x-1 color(red)(" Fail")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#(5x+1)(6x-1) = 30x^2-5x+6x-1 #

#= 30x^2+x-1 color(green)(" Works!")#