How do you factor the expression #10t^2 + 34t - 24#?

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Answer 1 · 2016-03-08T15:05:32

# color(blue)( (10t-6) (t+4)# is the factorised form of the expression.

#10t^2 +34t-24#

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 = 10*(-24) = -240#

AND

#N_1 +N_2 = b = 34#

After trying out a few numbers we get #N_1 = 40# and #N_2 =-6#
#40*(-6) = -240#, and #40+(-6)= 34#

#10t^2 +34t-24 =10t^2 +40t-6t-24 #

# = 10t (t+4) - 6(t+4)#

#(t+4)# is a common factor to each of the terms

# = (10t-6) (t+4)#

# color(blue)( (10t-6) (t+4)# is the factorised form of the expression.