Question

Factorize each of the following algebraic expression:
96 − 4x − x²

Answer 1

$$\begin{gathered} 96-4\mathrm{x}-{\mathrm{x}}^2 \\ =100-4-4\mathrm{x}-{\mathrm{x}}^2 \\ =100-({\mathrm{x}}^2+4\mathrm{x}+4) \\ =100-({\mathrm{x}}^2+2\times \mathrm{x}\times 2+2^2) \\ ={10}^2-(\mathrm{x}+2{)}^2 \\ =[10-(\mathrm{x}+2)\left]\right[10+(\mathrm{x}+2)] \\ =(10-\mathrm{x}-2\left)\right(10+\mathrm{x}+2) \\ =(8-\mathrm{x}\left)\right(12+\mathrm{x}) \\ =(x+12\left)\right(-x+8) \end{gathered}$$