How do you factor 8m² -34m -9 ?

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Answer 1 · 2015-05-17T08:20:16

#8m^2- 34m - 9#

We can Split the Middle Term of this expression to factorise it:

In this technique, if we have to factorise an expression like #am^2 + bm + c#, we need to think of 2 numbers such that:

#N_1*N_2 = axxc = 8xx(-9)= -72#

And,

#N_1 +N_2 = b = -34#

After trying out a few numbers we get #N_1 = -36# and #N_2 =2#
#(-36) xx 2 = -72#, and # -36 +2 = -34#

#8m^2- 34m - 9 = 8m^2- 36m + 2m - 9#

# = 4m(2m - 9) + 1(2m - 9)#

# = (4m + 1) (2m - 9) #
#color(green)((4m + 1) (2m - 9) )# is the Factorised form of #8m^2- 34m - 9#