Solve Trinomial Problem: 2(2x^2+3x-14)

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Homework Help Overview

The discussion revolves around factoring the trinomial expression 2(2x^2 + 3x - 14). Participants are exploring methods to factor the expression correctly without solving for x.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the intent to factor the trinomial rather than solve for x. There is mention of using the FOIL method, which leads to clarification about its application in multiplication rather than factoring. Various potential factor pairs for the trinomial are suggested, and one participant proposes starting with a general form of variables to match coefficients.

Discussion Status

The conversation is active, with participants providing insights and suggestions on how to approach the factoring process. Some guidance has been offered regarding the initial steps and considerations for factoring the expression, though there is no explicit consensus on the final factorization yet.

Contextual Notes

Participants note that the expression has already been partially factored by the leading coefficient of 2, and there is an emphasis on the possibility that the trinomial may not factor neatly with integer coefficients.

Hollysmoke
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I was working on this one trinomial problem-2(2x^2+3x-14) but I tried doing foil but I'm not sure what I am doing wrong. Could someone help me out? Thanks.
 
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Are you solving for x?
 
nope. Just trying to factor it.
 
Well, you can't be "solving for x" since there is no equation! Since you titled this "Factoring Problem", guess you want to factor it further. That "2" in front has already been factored out and you can ignore it (until you are ready to write the answer).

The first step, then, is to factor 2x2+ 3x- 14. When you say you tried "FOIL", I was puzzled for a moment- that's really a mnemonic for multiplying, not factoring. But I suspect you really mean is:
The only way to factor 2 (into integer factors) is 2 and 1 so you must have (2x )(x ). There are two ways to factor 14: 1*14 and 2*7 and since you have -14, that gives -1*14, 1*(-14), -2*7, and 2*(-7)
That is- if it is possible to factor 2x2+ 3x- 14 with integer coefficients it must be one of:
(2x- 1)(x+ 14)
(2x+ 1)(x- 14)
(2x- 2)(x+ 7)
(2x+ 2)(x- 7)
(2x+14)(x- 1)
(2x-14)(x+ 1)
(2x- 7)(x+ 2)
(2x+ 7)(x- 2)
(2x+ 1)(x-14)
(2x- 1)(x+ 14)

Go ahead, multiply them and see if any work. You really only need to check the "cross terms"- the "O" and "I" of FOIL. Of course, there is no guarantee that this can be factored with integer coefficients!

Once you've figured out how to factor 2x2+ 3x- 14, don't forget to write that "2" factor.
 
(2x+ 7)(x- 2)

Ahh thank you!
 
u could always start with variables (ax+b)*(cx+d) multiply through
match them to each coefficient and solve =]
 

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