Question

For how many values of k will x² + kx + 12 factor?

Answer 1

6

Explanation:

We want to factor the trinomial into a product of binomials. In general, we have ...

(x +a)(x +b) = x² +(a+b)x +ab

So, the values of "a" and "b" need to have a product of 12. There are 6 ways to do that:

12 = 1·12 = 2·6 = 3·4 = (-1)(-12) = (-2)(-6) = (-3)(-4)

The values of k are the sums of these factors of 12, so are

1+12 = 13

2+6 = 8

3+4 = 7

-1-12 = -13

-2-6 = -8

-3-4 = -7

There are 6 possible integer values of k that will make the trinomial factorable in integers:

k ∈ {-13, -8, -7, 7, 8, 13}