Answer:
1) For
:
and
, 2) For
:
and ![k = 12](https://tex.z-dn.net/?f=k%20%3D%2012)
Step-by-step explanation:
The polynomial
is a second-order polynomial of the form
. By direct comparison, we construct the following system of equations:
(1)
(2)
By (1) we know that there are a family of pairs such that the system of equations is satisfied. Let suppose that both
and
are integers. We assume two arbitrary integers for
:
1) ![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
![b = 7 - a](https://tex.z-dn.net/?f=b%20%3D%207%20-%20a)
![b = 6](https://tex.z-dn.net/?f=b%20%3D%206)
![a\cdot b = k](https://tex.z-dn.net/?f=a%5Ccdot%20b%20%3D%20k)
![k = (6)\cdot (1)](https://tex.z-dn.net/?f=k%20%3D%20%286%29%5Ccdot%20%281%29)
![k = 6](https://tex.z-dn.net/?f=k%20%3D%206)
2) ![a = 3](https://tex.z-dn.net/?f=a%20%3D%203)
![b = 7 - a](https://tex.z-dn.net/?f=b%20%3D%207%20-%20a)
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
![a\cdot b = k](https://tex.z-dn.net/?f=a%5Ccdot%20b%20%3D%20k)
![k = (3)\cdot (4)](https://tex.z-dn.net/?f=k%20%3D%20%283%29%5Ccdot%20%284%29)
![k = 12](https://tex.z-dn.net/?f=k%20%3D%2012)