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?
Mostly I'd say it's a custom, based on concepts of "neatness". But the factorization is not, in general, mathematically "necessary".Why do we have to factor the -1 out of the leading co-efficient?
E.g. –6x^2 – x + 2
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.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?