How do you factor #m^2+6m-27=0#?

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Answer 1 · 2015-09-20T16:45:28

#color(blue)((m-3)(m+9) # is the factorised form of the expression.

#m^2 +6m -27=0#

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 = a*c = 1 * -27 = -27#

AND

#N_1 +N_2 = b = 6#

After trying out a few numbers we get #N_1 = -3# and #N_2 =9#
#(9)*(-3) =-27# and #9+(-3)= 6#

#m^2 +6m -27=m^2 -3m +9m-27#

#=m(m-3) +9(m-3)#

#color(blue)((m-3)(m+9) # is the factorised form of the expression.