How do you factor #6t^2-17t+12=0#?

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Answer 1 · 2015-09-16T15:46:42

#color(blue)((3t-4)(2t - 3)#

#6t^2 -17t+12=0#

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

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

#N_1*N_2 = a*c = 6*12 = 72#
and
#N_1 +N_2 = b = -17#

After trying out a few numbers we get #N_1 = -9# and #N_2 =-8#
#(-9)*(-8 )= 72#, and #-9-8 =-17#

#6t^2 -17t+12=0#

#6t^2 -9t -8t+12=0#

#3t(2t - 3) -4(2t-3)=0#

#color(blue)((3t-4)(2t - 3)# is the factorised form of the expression.