How do you factor the expression #12s^2 + 6s - 6#?

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Answer 1 · 2016-07-20T05:33:39

#12s^2+6s-6=6(s+1)(2s-1)#

To factorize a quadratic polynomial such as #ax^2+bx+c=0#, one can spit middle term #b# in two parts whose product is #a×c#.

Hence, in #12s^2+6s-6#, one needs to split #+6# in two parts so that their product is #12×(-6)=-72# and these are #-6# and #12#.

Hence #12s^2+6s-6#

= #12s^2-6s+12s-6#

= #6s(2s-1)+6(2s-1)#

= #(6s+6)(2s-1)#

= #6(s+1)(2s-1)#