Determine the factors of x2 − 8x − 12.
(x − 6)(x + 2)
(x + 3)(x − 4)
Prime
(x + 6)(x − 2)

- anonymous

Determine the factors of x2 − 8x − 12.
(x − 6)(x + 2)
(x + 3)(x − 4)
Prime
(x + 6)(x − 2)

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- anonymous

Find two numbers that multiply to make your constant and add to make the coefficient of x

- anonymous

i think is is C

- anonymous

actually... none of those options seem to work... unless I dont know what im talking about anymore..

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## More answers

- hartnn

it does not have integral factors

- hartnn

because b^2 -4ac is not a perfect square

- anonymous

/;gt\

- hartnn

you can safely choose prime here....but it has irrational factors

- Jamierox4ev3r

so just for this question because of multiple choice, it would be prime, but it does have irrational factors..ha i should have known

- Jamierox4ev3r

now wonder i was confused okay :P

- hartnn

x = 8 +/- sqrt (108) /2

- hartnn

when
b^2-4ac is perfect square ----> integer roots
b^2-4ac is positive ----->real roots
b^2 -4ac is negative ---->imaginary roots --->prime

- hartnn

here, if domain of x is integer, only then we can consider it as prime

- Jamierox4ev3r

ahh okay then :)

- Jamierox4ev3r

very thorough explanation

- hartnn

) thanks!
i hope harlie got it ...

- DebbieG

Actually, I think the definition of a "prime polynomial" is when it cannot be factored into the product of two polynomials, using integer values. It doesn't mean that it "can't be written as a product" because any trinomial can, with rational, irrational or complex roots. :)

- anonymous

Nnope i still dont get it

- hartnn

which part ?

- anonymous

the one u said

- hartnn

you know what are a,b, c ?

- anonymous

is the answer A

- DebbieG

Did you check A by doing the FOIL multiplication, to see if you get back the original polynomial?

- DebbieG

You can check each answer by multiplying (one of the shortcomings of this kind of questions being multiple choice, since that doesn't teach you a darn thing about how to factor the polynomial).
But as @hartnn points out, the RIGOROUS way to show that it does not factor is to calculate the discriminant. He told you above what that tells you about the roots (and hence, the ability to factor).

- anonymous

I am not sure its because i only have 3 days to finish what i am doing so i need to know what is the answer

- DebbieG

Do you know how to FOIL multiply?

- DebbieG

(x − 6)(x + 2) = ???

- anonymous

x2 − 8x − 12.

- DebbieG

How did you get that? show me each of F-O-I-L steps.

- DebbieG

Meaning, show all 4 terms.

- anonymous

i didn't i just guessed

- DebbieG

Well, therein lies the problem. :) You aren't supposed to guess. Clearly, whatever the class is that you're in, this is material that you are expected to know. So if you don't learn how to do it, you will only get more and more behind.
FOIL mutliplication, remember this?
|dw:1377687867910:dw|

- DebbieG

So you get
(x)(x) + 2(x)-6(x) -6(2)

- anonymous

is it B

- DebbieG

Did you FOIL b to see if you get back to the original polynomial?

- DebbieG

(x + 3)(x − 4) = ?

- anonymous

idk

- DebbieG

Did you look at my example above on how to FOIL?
(x + 3)(x − 4) = x(x) -4(x) +3(x) -4(3) = ??

- DebbieG

If you don't remember how to FOIL multiply, then you really need to review that before you go any further. You are not prepared to do factoring problems, if you don't understand multiplying first.

- anonymous

i know how to use the FOIL METHOD

- DebbieG

You can review it here:
http://www.coolmath.com/algebra/03-polynomials/06-polynomials-multiplying-foil-01.htm

- DebbieG

Ok, that's good. Then why, when I asked:
(x + 3)(x − 4) = ?
Did you say "IDK"? Just FOIL it. :)

- anonymous

x2 − 8x − 12.

- DebbieG

No. Your middle term is wrong.

- DebbieG

(x + 3)(x − 4) = x(x) -4(x) +3(x) -4(3) = ??
-4(x) +3(x)\(\neq\)-8x

- anonymous

so it the last one

- DebbieG

Did you FOIL (x + 6)(x − 2) to check?

- DebbieG

(x + 6)(x − 2) = ??

- DebbieG

You need to know how to FOIL. IT'S IMPORTANT and if you don't, you will only be more and more lost when you get to the next topic. It's clear from the fact that you are being asked this problem that you are expected to know how to FOIL two binomials, and then how to factor ("un-FOIL") a trinomial. You can get this assignment turned in with every problem correct, but if you don't understand these basic concepts, you'll just be back here even more lost when you have to reduce a rational expression or find its domain, because you don't understand factoring a trinomial.

- anonymous

The answer prime

- DebbieG

Well, if you've checked the other 3 by correctly FOIL'ing them, and none of them work, then that would be all that's left.

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