Dimensions Of?
The volume, V(w) of a garden shed can be represented by the expression V(w) = w^3 – 10w^2 + 31w – 30, where w is the width of the garden shed in metres. Completely factor the expression. Find the dimensions of the garden shed.
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This factors as
(w-5)(w-3)(w-2)
but the volume is not given, but we know that the volume must be positive. Since this is positive cubic, we have positive values on (2,3) and (5, infinity).
The width must lie in one of these intervals, but we do not have enough information to determine that actual value.
Also note that the factorization is not necessarily the 3 dimensions of the shed. The question only says that this is a function of the width, and nothing is implied as to how the other two sides relate back to the width.
use synthetic division with w = 5, get w² – 5w + 6 as depressed equation, so factors are
(w – 5)(w – 3)(w – 2)
value of those factors depends on the volume, for which a value is not given.