How do you factor the trinomial #24k² + k - 3#?

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Answer 1 · 2016-04-25T17:12:27

#color(blue)((8k +3) ( 3k-1 ) # is the factorised form of the expression.

#24k^2 + k - 3#

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

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

#N_1*N_2 = a*c = 24 *(- 3) = -72#

AND

#N_1 +N_2 = b = 1#

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

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

#24k^2 + k - 3 = 24k^2 - 8k + 9k - 3#

#=8k ( 3k-1 ) +3 ( 3k - 1 )#

#(3k-1)# is a common factor to each of the terms

#= color(blue)((8k +3) ( 3k-1 ) #