Question

Franklin used the polynomial expression
x
(
x
−
3
)
(
x
+
4
)
to model the volume of a rectangular prism.



What is the length of the shortest side of this prism?


x


x
−
3


x
2
−
3
x


x
3
+
x
2
−
12
x

Answer 1

The factors give the three side lengths: x, x − 3, and x + 4. For a prism these must be positive, so x > 3, which makes x − 3 < x < x + 4. Thus the shortest side is x − 3.