How do you factor #3x^2 + 36x + 81#?

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Answer 1 · 2016-05-16T17:15:20

# (3x + 9 ) (x + 9 )# is the factorised form of the expression.

#3x^2 + 36x + 81#

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

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

#N_1*N_2 = a*c = 3* 81 = 243#

AND

#N_1 +N_2 = b = 36#

After trying out a few numbers we get #N_1 = 27# and #N_2 =9#
#27*9 = 243#, and #27+(9)= 36#

#3x^2 + 36x + 81 = 3x^2 + 27x + 9 x+ 81#

# = 3x(x + 9 ) + 9 ( x + 9 )#

#(x+9)# is a common factor to each of the terms

# = (3x + 9 ) (x + 9 )#