Question

if the volume of a cuboid is expressed as x^3-3x^2-9x-5, give

Answer 1

Given:

Volume of cuboid = x^3 - 3x^2 - 9x - 5 = p(x)

By trial and error method, we find that (x + 1) is a factor of x^3 - 3x^2 - 9x - 5. i.e., at x = -1, p(x) = 0.

Dividing (x^3 - 3x^2 - 9x - 5) by (x+1) gives us a quotient of (x^2 - 4x - 5)

Factorising (x^2 - 4x - 5) gives is (x - 5)*(x + 1)

Therefore factors of (x^3 - 3x^2 - 9x - 5) are (x - 5)*(x + 1)*(x + 1).

We can say that length, breadth and height of given cuboid are (x - 5), (x + 1) and (x + 1).

Answer 2

Here is the solution without division and shorter