# How do you simplify (2x^3-14x+2 )/(x+3)?

Jun 21, 2015

I agree with Jim that the expression maybe should have been

$\frac{2 {x}^{3} - 14 x + 12}{x + 3}$,

but let's see what happens with the one given...

#### Explanation:

$\frac{2 {x}^{3} - 14 x + 2}{x + 3}$

$= \frac{2 {x}^{3} + 6 {x}^{2} - 6 {x}^{2} - 18 x + 4 x + 12 - 10}{x + 3}$

$= \frac{\left(2 {x}^{2} - 6 x + 4\right) \left(x + 3\right) - 10}{x + 3}$

$= 2 {x}^{2} - 6 x + 4 - \frac{10}{x + 3}$

$= 2 \left(x - 2\right) \left(x - 1\right) - \frac{10}{x + 3}$

This doesn't really tell you much more than the original expression, and is not noticeably simpler.

It would be helpful if that $- \frac{10}{x + 3}$ remainder term were not there,

which is what would happen if the numerator were

$2 {x}^{3} - 14 x + 12$