How do you factor the trinomial #3c^2 - 1c - 24 #?

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Answer 1 · 2016-05-04T17:40:34

#color(green)((3c + 8) (c - 3) # is the factorised form of the expression.

#3c^2 - 1c - 24#

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

In this technique, if we have to factorise an expression like #xa^2 + ya + z#, we need to think of 2 numbers such that:

#N_1*N_2 = x*z= 3*(-24) = -72#

AND

#N_1 +N_2 = y = -1#

After trying out a few numbers we get #N_1 = -9# and #N_2 =8#

#(- 9)*8 = -72#, and #8 + (-9)= -1#

#3c^2 - 1c - 24 = 3c^2 - 9c + 8c - 24#

#=3c (c - 3) + 8 (c - 3)#

#= color(green)((3c + 8) (c - 3) #