I can't seem to figure out the answer to this problem:
11. the height of a rectangular prism is 5 more than three times it's width w. The volume of the prism is \(3w^2-4w^2-15w\). Write a simplified expression for the length of the prism.
Please help me as soon as possible!
I'm thinking that the volume is supposed to be 3w^3 - 4w^2 - 15
Let the width = w
Then the height is 3w + 5
And the volume is Width * Heiht * Length....so we have
3w^3 - 4w^2 - 15w = w * ( 3w + 5) * L
w (3w^2 - 4w - 15) = w (3w + 5) * L divide both sides by w
3w^2 - 4w - 15 = (3w + 5) * L factor the left side
(3w+ 5) (w - 3) = (3w + 5) * L divide both sides by (3w + 5)
(w - 3) = L = Length