How do you factor #2x^2-5x-12 #?

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Answer 1 · 2015-08-05T13:52:14

#=color(green)((2x+3)(x-4)#

#2x^2−5x−12#

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

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

#N_1*N_2 = a*c = 2*-12 = -24#
and,
#N_1 +N_2 = b = -5#

After trying out a few numbers we get:
#N_1 = -8# and #N_2 =3#
#3*(-8) = -24#, and
#3+(-8)= -5#

#2x^2−color(blue)(5x)−12 = 2x^2−color(blue)(8x +3x)−12#

# = 2x(x-4) +3(x-4)#

#(x-4)# is a common factor to each of the terms

#=color(green)((2x+3)(x-4)#