Question

Write a polynomial that represents the product of three consecutive odd integers,the first one being (2x - 1).

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{integer}=\left(2x-1\right) \\ \mathrm{Then}\mathrm{second}\mathrm{integer}=2x \\ \mathrm{Then}\mathrm{third}\mathrm{integer}=\left(2x+1\right) \\ \mathrm{Product}\mathrm{of}3\mathrm{integers}=\left(2x\right)\left(2x-1\right)\left(2x+1\right)=2x\left[4x^2-1\right]=8x^3-2x \\ \mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{polynomial}=8x^3-2x \end{gathered}$$