The volume of a rectangular prism with a square base can be expressed x^3+8x^2+16. What are the dimensions of the prism in terms of x? Show or explain your work.

Answer 1

V = Bh, and B has to be "something" squared since the base is a square.

The factors of 16 that are perfect squares themselves are 1, 4 and 16.

h is going to be x plus something because squaring the dimensions of the base gives us a positive number and we have a positive 16 as our final result.

So, our options are...

(x - 1)(x - 1)(x + 16)

(x + 1)(x + 1)(x + 16)

(x - 2)(x - 2)(x + 4)

(x + 2)(x + 2)(x + 4)

(x - 4)(x - 4)((x + 1)

(x + 4)(x + 4)(x + 1)

All we have to do is add the constants to see which adds up to 8. -1 + (-1) + 16 ≠ 8, so that's not it.

I bet you can find it from here!