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

- anonymous

- katieb

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- klimenkov

what means using integers?

- klimenkov

Integer roots or integer value of k?

- anonymous

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...

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## More answers

- klimenkov

For the first one: -18, 18.

- anonymous

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

- klimenkov

Do you know Vieta's Theorem?

- anonymous

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...

- anonymous

So you factor it out into 2 binomials?

- klimenkov

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

- anonymous

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 =_=

- anonymous

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

- anonymous

Thanks for helping me~

- anonymous

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

- anonymous

See you guys around^^ Bye

- 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.

- klimenkov

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

- klimenkov

Or she.

- 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.

- klimenkov

Oops. Sorry, it's not right.

- 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 \(a\).

- 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.

- klimenkov

\(k>0\) in the statement.

- klimenkov

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

- klimenkov

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

- 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.

- anonymous

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

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