Question 1178730
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I'm seeing a number of similar questions on this forum about factoring polynomials with a negative leading coefficient.  Here are my thoughts about this.<br>
An internet search shows me that it is customary (?) to call the greatest common factor of a polynomial negative if the leading coefficient is negative; for example<br>
{{{-3x^2+9x+6 = -3(x^2-3x-2)}}} instead of {{{-3x^2+9x+6 = 3(-x^2+3x+2)}}}<br>
Apparently your son has been taught this ("During factoring we factor the negative sign of the leading coefficient...").<br>
My comment is that in fact the factoring of a polynomial is not the solution to a problem; it is only a step in solving a problem.  Whether or not you include the negative as part of the GCF is of no importance at all.  In working some kinds of problems, NOT including the negative as part of the GCF might make solving the whole problem easier.<br>
What is REALLY troubling is that it appears your son is being taught that the negative of a leading coefficient should be factored out, but when he does that with this problem to factor 81-x^2 as -(x+9)(x-9), he is told that his answer is wrong.<br>
OF COURSE a student just learning a subject will be confused if he is being told things like that!!<br>
Unfortunately, what is going on here is simply BAD TEACHING.<br>
Again, the factoring itself is not the end goal; it is a step in solving an actual problem.  And for that purpose, and answer of -(x+9)(x-9) is every bit as good as (9+x)(9-x).<br>