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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