A box has a width 9 inches less than its height and a length 7 inches more than its height.

a. If h is the height of the box, write a polynomial that represents the volume of the box.

b. Use this polynomial to calculate the volume for h = 17 inches.

So everything in this problem is in terms of height (h). We'll abbreviate width to w and length to l and volume to v

l=h+7

w=h-9

a.

volume is height x width x length

v=h * (h+7) * (h-9)

now we have to multiply these values

h * (h+7) = h^2+7h

(h^2+7h) * (h-9) = h^3-9h^2+7h^2-63h=h^3-2h^2-63h

b.

now we plug in h=17

v=17^3 - 2 (17) ^2 - 63 (17) = which comes out to 2686

note: * * i suggest going through these steps on your own mostly because it's late and i'm tired and that seems like an awfully large number so you may want to check it