How do you find all values of k so that the polynomial x^2+kx-19x2+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 m=1,a=c=±1 - since
p=19, bd=19p=19,bd=19 , so we can have eitherb=+-1, d=+-19b=±1,d=±19 , with the signs moving in concert (so if b is positive, d is positive). And sob+d=+-20b+d=±20
and so this means that for:
We can have:
And so
