Why are quadratics factored into 2 brackets? Why is it that no one seems to factor quadratics into just one bracket Eg:
$$2x^2+8x+6$$
into
$$2x\left(x+4+3\cdot\frac{1}{x}\right)\quad\text{or}\quad 2x\left(x+4+\frac{3}{x}\right)\quad ?$$

Here's a few reasons:


*

*No one likes division. It is difficult.

*This factoring doesn't tell you what the roots might be.

*Either way you have $4$ "terms."

*It is not as neat.

*Note that: $2x(x+8+3\cdot \frac{1}{x}) = (2x)(x+8+3\cdot \frac{1}{x})$
