How do you divide (x^3 +1) by (x^2 + 2x)?

Question

Thank you for your answers. They were very helpful

Answer 1

Like a normal division problem:

_______ x - 2
x^2 + 2 x | x^3+ 0x^2 + 0x + 1
________x^3 + 2x^2
________0x^3- 2x^2 + 0x
____________-2x^2 - 4x
____________0x^2 + 4x + 1
_______________R= 4x+1

(x^3+1)/(x^2+2x) = x - 2 + (4x+1)/(x^2+2x)

Answer 2

x^2 + 2x ) x^3 + 0X^2 + 0x + 1 (x - 2
x^3 + 2x^2 (Subtract)
__________
0x^3 - 2x^2 + 0x
-2x^2 - 4x (subtract)
_________
0x^2 + 4x + 1 remainder

So answer is x -2 with a remainder of 4x +1

Answer 3

Think of it this way...
(x*x*x)+1
---------------
(x*x)+(2*x)

So, the first 2 xs on the top and bottom cancel out leaving you with:

x+1
-----
x*2 And that's your answer.