How do you factor the trinomial #9r^2+15r+6#?

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Answer 1 · 2016-02-23T17:32:36

#= (9 r +6) ( r +1) #

#9r^2 +15r +6#

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

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

#N_1*N_2 = a*c = 9*6 =54#
AND
#N_1 +N_2 = b = 15#

After trying out a few numbers we get #N_1 = 6# and #N_2 =9#
#9*6 = 54# , and #9 +6=15#

#9r^2 +15r +6 =9r^2 +9r +6r +6 #

#= 9 r ( r +1) +6 (r +1 ) #

#= (9 r +6) ( r +1) #