show all work. find the quotient. y^4 +8y -1 / y^2 + 4

Question

show all work. find the quotient.  y^4 +8y -1 / y^2 + 4

callisto · Answer

y^2 - 4
            ---------------------
y^2 +4 )  y^4                +8y   -1
               y^4  + 4y^2
              ---------------------
                      -4y^2    +8y      -1
                      -4y^2               -16
                     -----------------
                                     8y +15
So what is the quotient?

anonymous · Answer

Callisto, thank you so much. I kept getting stuck as to how to write out the part after the subtraction.  i'm still not sure about the very last part, i know there is a remainder left over

callisto · Answer

and do you understand now?

anonymous · Answer

kind of, these really throw me. this is the only one i've really had trouble with

callisto · Answer

which was the part that you didn't (don't) understand?

anonymous · Answer

how to write it out and put everything where it goes and how to write out the answer with the  remainder. So would the answer for the quotient written out be (y^2-4)+(8y+15/y^2+4) or can that be broken down further

callisto · Answer

---------------------------------
(things on the bottom) ) (things on the top)

anonymous · Answer

i'm not sure i understand what you mean (things on the bottom))(things on the top)

anonymous · Answer

so when i write my answer i should just leave it with the remainder at the bottom rather than trying to write it out as an expression

callisto · Answer

can you try (2x^3+5x^2 +14)/(x+2)?

anonymous · Answer

i can get as far as getting 2x^2+2, but then i get confused as to how to carry it down to get the rest of the answer. this is my first time taking algebra and the first thing i just can't seem to learn about it

callisto · Answer

can you show your steps?

anonymous · Answer

______2x^2__+ 2_________
x+2) 2x^3        +5x + 14
        2x^3+2
        ___________________________
                 +2  + 5x  + 14
                           4x   +  4

anonymous · Answer

i know i have to be doing something wrong but not sure what

callisto · Answer

_2x^2_-4x_______13___________
x+2) 2x^3                   +5x + 14
        2x^3+2(2x^2)
        ___________________________
                 -2(2x^2)  + 5x  + 14
                 -4x^2      -8x          
        ------------------------
                                 13x +14
                                 13x +26
                                 ---------
                                          -12

callisto · Answer

sorry for late reply

anonymous · Answer

it's okay, i was working on the rest of my problems

callisto · Answer

Nah.. originally, it should be a 5x^2... anyway ,just change it to 5x then :D

anonymous · Answer

ok, i think i see what it is i'm doing wrong now, especially since you put the (2x^2) in.

callisto · Answer

I hope you will understand...

anonymous · Answer

i hope so too, thank you for all your help, you're the best!!!

callisto · Answer

welcome, but i'm certainly not the best, there are many great people here :D