Question

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

Answer 1

`(4x^2+8x+16)/(x-2) = 4x+16 " 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 `(-2)` 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") :}#