Factoring ax^2 + bx + c

Question

Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trimonials.

4n^2+ __n - 3

Please explain and solve.

Answer 1

I multiplied the first and last to get -12
(4)(-3) = -12

now what factors give me -12 ?
could be 4, -3 or -4, 3 or 6, -2 or -6, 2

for each pair, their sum has to go in the middle, so
we could have:
4n^2 + n - 3
4n^2 -n - 4
4n^2 + 4n - 3
4n^2 - 4n - 3

each of these WILL factor
e.g.
4n^2 + 4n - 3 = (2n-1)(2n+3)