Question 1203033
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A field has an area of x^2 + x-6. State the expressions for its length and width.
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        The problem formulation is not precisely correct, 

        because there are infinitely many answers - - - much more answers than one.



<pre>
One possible answer is  x^2 + x - 6 = (x^2 + x - 6)*1, giving the dimensions

    (x^2 + x - 6)  and 1 (one unit)

that are valid when the quadratic is positive (x > 2 or x < -3).



Another possible decomposition/factoring is  x^2 + x - 6 = (x+3)*(x-2), 
which gives the dimensions (x+3) and (x-2) linear units with x > 2.



Third possible decomposition/factoring is  x^2 + x - 6 = {{{(a*(x+3))*((1/a)*(x-2))}}}, 
which gives the dimensions a*(x+3) and {{{(1/a)*(x-2)}}} linear units with x > 2 
and any real number "a".
</pre>

Solved, with explanations.


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The error in the problem formulation is TYPICAL for such problems,
made by unexperienced Math problems composers, or those who copy-paste from other sources
without thinking on the subject.


I saw such errors many times (more than I can count :).