Question

Volume of a cuboid is $7x^2-56x+105$ cubic units, then the possible dimensions of the cuboid are________,________ and _______ given that $x>5$.

Answer 1

Finding dimension of cuboid:

To find the dimension of cuboid we factorize the polynomial.

Volume of cuboid is given to be $7x^2-56x+105$.

$7x^2-56x+105$$=7\left(x^2-8x+15\right)$

$$\begin{gathered} =7\left(x^2-3x-5x+15\right) \\ =7\left[x\left(x-3\right)-5\left(x-3\right)\right] \\ =7\left(x-3\right)\left(x-5\right) \end{gathered}$$

Hence, for volume of a cuboid is $7x^2-56x+105$ cubic units, then the possible dimensions of the cuboid are the dimension of cuboid are $7,\left(x-3\right)\mathrm{and}\left(x-5\right)$ given that $x>5$.