# How do you divide (4x^2+8x+16) / (x-2) ?

Oct 28, 2015

$\frac{4 {x}^{2} + 8 x + 16}{x - 2} = 4 x + 16 \text{ with a remainder of } 48$

#### Explanation:

This can be done by polynomial long division or synthetic division.

Using synthetic division (because it is easier to format here)
[Remember that when dividing by a monic binomial the multiplicative value is the negative of the constant; in this case the negative of $\left(- 2\right)$ is $+ 2$

{: (,,x^2,x^1,x^0), (,"|",4,+8,+16), (+,"|", ,8 ,32), (xx(+2),"|",color(red)(4),color(red)(16),color(blue)(48)), (,,x^1,x^0,"Remainder") :}