Facotring the -1 out of the leading co-efficent?  TOPIC_SOLVED

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Facotring the -1 out of the leading co-efficent?

Postby qwertyuiop123 on Fri Feb 17, 2012 9:56 pm

Why do we have to factor the -1 out of the leading co-efficient?
E.g. –6x^2 – x + 2


Also, consider this example:
Factorize 2x + 4
That would be 2(x+2)
Can't it also be -2(-x-2) ??
Which one is correct? Why?
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Postby stapel_eliz on Sat Feb 18, 2012 12:06 pm

qwertyuiop123 wrote:Why do we have to factor the -1 out of the leading co-efficient?
E.g. –6x^2 – x + 2

Mostly I'd say it's a custom, based on concepts of "neatness". But the factorization is not, in general, mathematically "necessary".

qwertyuiop123 wrote:Also, consider this example:
Factorize 2x + 4
That would be 2(x+2)
Can't it also be -2(-x-2) ??
Which one is correct? Why?

Mathematically, they are equivalent. But the first factorization is considered "neater" and "more simplified" than the second. It's kind of like polynomials being written "correctly" only when they're written with the terms in descending order, as you have done above. It's convention.

That said, "the right answer" is often "what the teacher wants to see". So if your instructor considers the "neat" form to be "correct", then that's how you'll need to format things. It's like there being no law that requires one-inch margins on papers, but English teachers may require this. :wink:
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