Answer:
B The length is 5 inches, the width is 2 inches, and the height is 14 inches.
Step-by-step explanation:
The equation that desribes the volume of a party-favor bag is
[tex]x^3+6x^2-27x-140=0.[/tex]
The solutions of theis equation can be found among divisors of -140. The divisors are:
[tex]\pm1, \pm2, \pm4, \pm5, \pm 7,\pm 10, \pm 14, \pm 20, \pm 35, \pm 70, \pm 140.[/tex]
Note that
[tex]5^3+6\cdot 5^2-27\cdot 5-140=125+150-135-140=275-275=0,[/tex]
so
[tex]x=5[/tex]
is the solution of the equation.
Hence,
the length is 5 inches, the width is 5-3=2 inches and the height is 5+9=14 inches.
