## MissKelly~ 2 years ago Find all values of k so that each polynomial can be factored using integers. 1.) x^2+kx-19 2.) x^2 - 8x+k, k>0

1. klimenkov

what means using integers?

2. klimenkov

Integer roots or integer value of k?

3. MissKelly~

I don't know...I just wrote word for word for what it says in the book...All I know is that for #1 the answers will be in integers...

4. klimenkov

For the first one: -18, 18.

5. MissKelly~

How do you solve it? Distributive...factor?

6. klimenkov

Do you know Vieta's Theorem?

7. MissKelly~

Not yet, The questions I got was from the book on the chapter of Quadratic equations, and it said it required Higher-order thinking skills...

8. MissKelly~

So you factor it out into 2 binomials?

9. klimenkov

Vieta's Theorem is not so hard to get. I advice you to get it and try to use for your task.

10. MissKelly~

I'm not so sure my teacher wants me to apply Vieta's Theorem yet, because she hates it when we move on ahead of her teachings...btw she can't teach =_=

11. MissKelly~

Well I have to leave for school in a little while, there's a chemical equation quiz waiting for me...

12. MissKelly~

Thanks for helping me~

13. MissKelly~

Hehe why is that? Well I'm sorry I have to go to school now..

14. MissKelly~

See you guys around^^ Bye

15. klimenkov

If you want to factor \(x^2+kx-19\), I hope you will think it will be \((x-a)(x-b)\). So, when expanding: \(x^2-(a+b)x+ab\). Now just look at the coefficients. \(k=-(a+b), -19=ab\). You want only integers. From the second equality it will be only \(a=1,b=-19\) or \(a=19,b=-1\), because 19 is a prime number. Now try to find \(k\) in both cases.

16. klimenkov

Just try to explain. Not so sure he got it.

17. klimenkov

Or she.

18. klimenkov

If \(-(a+b)=-8\), so \(a+b=8\). And \(ab=k\), we get \(a(8-a)=k>0\). It will be if \(-a^2+8a>0\).|dw:1357824979524:dw| Answer: 1, 2, 3, 4, 5, 6, 7.

19. klimenkov

Oops. Sorry, it's not right.

20. klimenkov

The answer will be if you put all this numbers: 1, 2, 3, 4, 5, 6, 7 in the expression for \(k=a(8-a)\) instead of \(a\).

21. klimenkov

How did you get that this will be all the possible values for \(k\), that you've written k = {0, 7, 12, 15, 16}? \(k=0\) doesn't suit.

22. klimenkov

\(k>0\) in the statement.

23. klimenkov

I can't be absolutely sure that this will be ALL the values for \(k\) by just guessing its value.

24. klimenkov

The source of our misunderstanding is my bad English. Sometimes I can't get what is spoken about.

25. klimenkov

You say that it is no need in writing \(k=a(8-a), a=1,2,\ldots ,7\). Because it will have the same value for \(a=1\) and \(a=7\). I just showed the way I had solved this task. Sorry.

26. MissKelly~

Okay I'm back...whoooooa. And yeah I got it now^^