Choose three integers a, b, and c. (Negative numbers are welcome.)?

Question

Now use a, b, and c to create a
trinomial ax2+bx+c. Can you factor this trinomial? How would you create a trinomial that will factor?

Answer 1

Let a = 1, b = -1 and c = -2
Then x²-x - 2 = (x+1)(x-2).
In general you can create a trinomial that will
factor over the integers by choosing a,b and c
so that b²-4ac is a square.
Example: x²-x-12. Here b²-4ac = 49 = 7²,
so x²-x-12 factors into (x+3)(x-4).