How do you factor #5d^2-4d-1#?

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Answer 1 · 2016-05-08T17:18:28

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

#5d^2 -4d - 1#

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

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

#N_1*N_2 = a*c = 5* (- 1) = -5#

AND

#N_1 +N_2 = b = -4#

After trying out a few numbers we get #N_1 = -5# and #N_2 =1#
#(-5)*(1) = -5#, and #1 +(-5)= -4#

#5d^2 -4d - 1 =5d^2 -5d + 1d - 1#

#=5d ( d - 1 )+ 1 (d - 1)#

#(d-1)# is a common factor to each of the terms:

# = color(blue)( (5d +1 ) ( d - 1 ) #