How do you factor #4v^2-9v-9#?

1 Answer
Alan P.
Apr 14, 2015

#4v^2-9v-9#

#=(4v-3)(v+3)#

But how to get there is a little more complex.

Start by looking at factor pairs of #4#
(that is values #(a,b)# such that #axxb=4#)
and
factor pairs of #9#
(again, values #(p,q)# such that #pxxq=9#)

There are only a very few possibilities
#4 = (4xx1)# or #(2xx2)# or negative versions of these pairs
#-9 = (9xx-1)# or #(3,-3)# or negative versions of these pairs

We are looking for values #(a,b)# and #(p,q)#
such that
#(av+p)(bv+q) = 4v^2 -9v -9#

Because of our restrictions on possible factor pair values
we simply need to find the two pair factors that give
#aq+bp = -9#

Since there are not a lot of combinations
the two pairs #(4,1)# and #(-3,3)# soon become obvious.

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