long division with polynomials?

Question

4x^5 +8x^4 -8x^3 +4x^2 +x-8 / 5x^2 -4x+9

when trying to do the division I got 4/5x^3 for the first term but couldnt get past that. help!

both of those answers are incorrect!

Answer 1

I'll try to help...

First, I'm going to leave out all the x-terms, but just imagine they are there:

.................. ........ ......4/5 56/25 -156/125 -1028/625
5 ... -4 ... 9 ) 4 ... 8 ... -8 ... 4 ... 1 ... -8
................... 4 .-16/5 36/5
...................------------------
................... ......56/5 -76/5 4
................... ......56/5 -224/25 504/25
................... ......-------------- -----------
................... ............. -156/25 -404/25 1
................... ............. -156/25 624/125 -1404/125
................... ............. ------------------- ----------------
................... ............. ........... -1028/125 1529/125 -8
................... ............. ........... -1028/125 4112/625 -9252/625
................... ............. ........... ------------- --------------- --------------
................... ............. ................. .......... 3553/625 4252/625

If I did it correctly (which there is no guarantee), I get the answer as:

(4/5)x^3 + (56/25)x^2 - (156/125)x - 1028/625)
with a remainder of:
[ (3553/625)x + 4252/625 ] / (5x^2 -4x+9)

However, with all those fractions I probably made a mistake somewhere... your math teacher is a masochist!

Answer 2

4/5x^3+56/25x^2 +148/25x + 188/125
________________________
5x^2 -4x+9 / 4x^5 + 8x^4 - 8x^3 + 4x^2 + x - 8
4x^5 - 16/5x^4 + 36/5x^3
--------------------------------
56/5x^4 - 76/5x^3 + 4x^2
56/5x^4 -224/25x^3 +504/25x^2
-----------------------------------------
148/5x^3 - 404/25x^2 + x
148/5x^3 - 592/25x^2 + 5328/5x
-----------------------------------------
188/25x^2 - 5323/5x+8
188/25x^2-752/125x
+1692/125
----------------------------------
-1058.584x - 5.536


The answer is

4/5x^3+56/25x^2 +148/25x + 188/125 -
1058.584x + 5.536
-----------------------
5x^2 -4x+9

I hope this is correct!
PLS TELL ME IF THIS IS NOT CORRECT.

I did not review my answer.