How do you factor #12x^2-4x-40#?

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Answer 1 · 2016-05-01T16:55:28

# color(blue)((12x + 20 ) (x-2) # is the factorised form of the expression.

#12x^2 - 4x - 40#

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 = 12*(-40) = -480#

AND

#N_1 +N_2 = b = -4#

After trying out a few numbers we get #N_1 = 20# and #N_2 =-24#
#20 *(- 24) = - 480#, and #20+(-24)= -4#

#12x^2 - 4x - 40 = 12x^2 - 24 x + 20x - 40#

# = 12x(x-2) + 20 ( x-2)#

#(x-2)# is a common factor to each of the terms
# color(blue)((12x + 20 ) (x-2) # is the factorised form of the expression.