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

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
qwertyuiop123
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### Facotring the -1 out of the leading co-efficent?

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?

stapel_eliz
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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".
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.