How do you factor #36a^2-3a-5#?

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Answer 1 · 2016-05-05T17:13:53

# color(blue)((3a + 1) (12a - 5) # is the factorised form of the expression.

#36 a^2 - 3a - 5#

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

In this technique, if we have to factorise an expression like #xa^2 + ya + z#, we need to think of 2 numbers such that:

#N_1*N_2 = x*z = 36 * (-5) = -180#

AND

#N_1 +N_2 = b = -3#

After trying out a few numbers we get #N_1 = -15# and #N_2 =12#

#12*(-15) = -180#, and #12+(-15)= -3#

#36 a^2 - 3a - 5= 36 a^2 - 15a + 12a - 5#

#= 3a (12a - 5) + 1 ( 12a - 5)#

# = color(blue)((3a + 1) (12a - 5) #