Factoring Question: Why not factor x^2+2x+1 as (-x-1)(-x-1)?

mlbrewer

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Why not factor x^2+2x+1 as (-x-1)(-x-1)? I have some students coming to me doing this and wonder why.
 

Subhotosh Khan

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Why not factor x^2+2x+1 as (-x-1)(-x-1)? I have some students coming to me doing this and wonder why.
You can ... which same as factoring -1 out of each factor and multiplying.
 

Dr.Peterson

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Why not factor x^2+2x+1 as (-x-1)(-x-1)? I have some students coming to me doing this and wonder why.
In the same way, you could factor 6 as (-2)(-3). It's not wrong, just different.

I recommend, for several reasons, always factoring so that the leading terms are positive. This preference makes many tasks easier; for instance, it avoids problems in factoring by grouping. It is not the only valid answer, but is a good habit.

As to why they do it -- ask them! I'd be interested to know. I suppose somehow -1 catches their attention first. Or maybe they just like being different!
 
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