Question

Find all integers k such that the trinomial can be factored over the integers. (Enter your answers as a comma-separated list.)
2x2 + kx – 3

Answer 1

Hmm... i think you should look for all the pairs of numbers a and b such that:\[ab=-6\]since 2 times -3 is negative 6. This gives:

1,-6
-1,6
2,-3
-2,3

Thats it (not including the reverse of those pairs). Now adding the two numbers in each pair gives;

-5
5
-1
1

So those are the values of k which will let the polynomial be factored. Im not sure if there are any others though =/