Factoring Trinomials

[hthompson74]

Hello, my problem is 3x^2 - 4x - 14

I know that I must find the factors of -14, which then should also add up to 4, however, this seems impossible to me since the only factors I can come up with are (-1,14)(-14,1)(2,-7) and (-7,2).
Then the coefficient of 3..should it be included in the first set of parenthesis like (3x+?)(x-?_) or kept as a coefficient like 3(x+?)(x-?). Perhaps the error is in the problem and it should have been -5x in there. Now that would make more sense. Any help would be greatly appreciated. Thank you.

 

[Deleted member 4993]

Hello, my problem is 3x^2 - 4x - 14

I know that I must find the factors of -14, which then should also add up to 4, however, this seems impossible to me since the only factors I can come up with are (-1,14)(-14,1)(2,-7) and (-7,2).
Then the coefficient of 3..should it be included in the first set of parenthesis like (3x+?)(x-?_) or kept as a coefficient like 3(x+?)(x-?). Perhaps the error is in the problem and it should have been -5x in there. Now that would make more sense. Any help would be greatly appreciated. Thank you.

The roots of this function are irrational.

So it cannot be factorized by the method (you are trying to use).

 

[stapel]

Hello, my problem is 3x^2 - 4x - 14

I know that I must find the factors of -14, which then should also add up to 4....

Actually, you need to find the factors of (3)(-14) = -42 that add to -4.

And, as noted in a previous reply, there aren't any factors that work, so this is "prime over the integers" (or, in terms of your studies at this point, "unfactorable").

 

[Deleted member 4993]

or it could be:

3x^2 - x - 14 → (3x - 7)(x+2)

or

3x^2 + x - 14 → (3x+7)(x-2)

or some such variation.....