Question

the volume of a cuboid is given by the polynomial p[x] = 8x³ + 12x²- 2x-3 . Find possible expression for the dimensions of the cuboid. Verify THE RESULT BY taking x= 5 units

Answer 1

$$\begin{gathered} \mathrm{p}\left(\mathrm{x}\right)=8{\mathrm{x}}^3+12{\mathrm{x}}^2-2\mathrm{x}-3 \\ =4{\mathrm{x}}^2\left(2\mathrm{x}+3\right)-1\left(2\mathrm{x}+3\right) \\ =\left(4{\mathrm{x}}^2-1\right)\left(2\mathrm{x}+3\right) \\ =\left(2\mathrm{x}+1\right)\left(2\mathrm{x}-1\right)\left(2\mathrm{x}+3\right) \\ \mathrm{So}, \\ \mathrm{Dimension}\mathrm{of}\mathrm{cuboid}\mathrm{are}\left(2\mathrm{x}+1\right),\left(2\mathrm{x}-1\right)\mathrm{and}\left(2\mathrm{x}+3\right). \\ \mathrm{For}\mathrm{x}=5 \\ \mathrm{Dimensions}\mathrm{are} \\ \left(2\left(5\right)+1\right),\left(2\left(5\right)-1\right)\mathrm{and}\left(2\left(5\right)+3\right) \\ 11,9\mathrm{and}13. \end{gathered}$$