# How do you find all values of k so that the polynomial #x^2+kx-19# can be factored with integers?

##### 1 Answer

Dec 23, 2016

#### Explanation:

When we factor a trinomial of form

we end up with a general form:

where:

So let's now move to the statement in question:

And so we have:

We're asked to show all values of

From this, we know that:

- since
#m=1, a=c=+-1 # - since
#p=19, bd=19# , so we can have either#b=+-1, d=+-19# , with the signs moving in concert (so if b is positive, d is positive). And so#b+d=+-20#

and so this means that for:

We can have:

And so