Mathematics
OpenStudy (anonymous):

(8x^4+nx^3-8x^2-x-19)/(2x+5) solve n when remainder is -4

OpenStudy (anonymous):

answer i have 125/32 but it's saying it's wrong i dont know why

OpenStudy (anonymous):

this looks like a pain. I would replace x by $-\frac{5}{2}$ and set the result = -4 and solve for n was that the method you used?

OpenStudy (anonymous):

exact same remainder theorem

OpenStudy (anonymous):

i get -64n+246=-4

OpenStudy (anonymous):

let me try something with pencil and paper and see what happens

OpenStudy (anonymous):

thnk u satellite

OpenStudy (anonymous):

oh maybe you have to divide by 2. hold on a minute i can't work on the screen

OpenStudy (anonymous):

lol ok

OpenStudy (anonymous):

because synthetic division only works if the leading coefficient is 1. that is why it probably did not work. i am trying it long hand

OpenStudy (anonymous):

uh why are u doing synthetic division?

OpenStudy (anonymous):

or long division i thought question was supposed to use remainder theorem

OpenStudy (amistre64):

id divide it out to see what the "equation" for the remainder would be; set that equal to -4

OpenStudy (anonymous):

yes but if you replace x by 5/2 you are ignoring the fact that you are dividing by 2x+5 it is as if you are dividing by $x+\frac{5}{2}$

OpenStudy (anonymous):

ok.............

OpenStudy (zarkon):

16

OpenStudy (anonymous):

i divided the numerator and denominator by 2, the evaluated as 5/2 so far i have $269+\frac{n}{2}\times (\frac{5}{2})^3=-4$ and will try from here

OpenStudy (anonymous):

ok zarkon what snap method did you use?

OpenStudy (anonymous):

satellite ur way i get -4368/125

OpenStudy (anonymous):

how did zarkon get 16?

OpenStudy (anonymous):

i calculated wrong let me try again slowly. in the meantime maybe zarkon will show the snap way

OpenStudy (anonymous):

CALLING ON ZARKON!!

OpenStudy (anonymous):

or actually ny1 who can explain how to get the correct answer

OpenStudy (anonymous):

16 is correct. now let me see if my feeble mind can find it quickly

OpenStudy (zarkon):

i'm trying to find a nice way to get the answer...I don't want to type up what i did

OpenStudy (anonymous):

Lol

OpenStudy (amistre64):

4x^3+(n-20)x^2/2+(-5n+84)x/4+(25n -424)/8 ------------------------- 2x+5 | 8x^4 +nx^3 -8x^2 -x -19 -8x^4 -20 x^3 --------------- (n-20)x^3 ( -16)x^2/2 -(n-20)x^3 (-5n +100)x^2/2 --------------------------- (-5n +84)x^2/2 (-4)x/4 (25n-420)x/4 -------------- (25n -424)x/4 (-152)/8 (-125n+2120)/8 ---------------- (-125n+2068)/8 -125n+2068 ----------- = -4 8(2x+5) i cant tell if i did it right or not :)

OpenStudy (amistre64):

ack .. remainder = -4 so -125n + 2068 = -4 then?

OpenStudy (anonymous):

^according to u it very close n=16.576

OpenStudy (anonymous):

@zarkon can you just say what you did? i divide numerator and denominator by 2, replace x by -5/2 and then set result = -4

OpenStudy (anonymous):

Zarkon u there?

OpenStudy (zarkon):

solve $246-\frac{125n}{8}=-4$

OpenStudy (zarkon):

$8x^4+nx^3-8x^2-x-19|_{x=-5/2}=246-\frac{125n}{8}$

OpenStudy (anonymous):

nvm my stupidity to the max i was plugging in -4 in the nx^3 FML

OpenStudy (anonymous):

i tried that but it didn't work!

OpenStudy (anonymous):

it works

OpenStudy (anonymous):

wow i marvel at my own stupidity sometimes

OpenStudy (anonymous):

oh i guess it helps if you type -5/2 instead of 5/2 <dopeslap>

OpenStudy (anonymous):

thnkx zarkon

OpenStudy (amistre64):

.... that was my first thought; but figured why not kill a few brain cells along the way :)

OpenStudy (zarkon):

$\frac{8x^4+nx^3-8x^2-x-19}{2x+5}=g(x)+\frac{-4}{2x+5}$ $8x^4+nx^3-8x^2-x-19=g(x)(2x+5)-4$ evaluate at x=-5/2 and solve for n I believe this is what satellite73 was doing ?

OpenStudy (anonymous):

yah but i typed in 5/2 so answer was all screwed up.

jimthompson5910 (jim_thompson5910):

$\large 8x^4+nx^3-8x^2-x-19=-4$ $\large 8\left(-\frac{5}{2}\right)^4+n*\left(-\frac{5}{2}\right)^3-8\left(-\frac{5}{2}\right)^2-\left(-\frac{5}{2}\right)-19=-4$ $\large 8\left(\frac{625}{16}\right)+n*\left(-\frac{125}{8}\right)-8\left(\frac{25}{4}\right)-\left(-\frac{5}{2}\right)-19=-4$ $\large \frac{5000}{16}-\frac{125n}{8}-\frac{200}{4}+\frac{5}{2}-19=-4$ $\large \frac{625}{2}-\frac{125n}{8}-50+\frac{5}{2}-19=-4$ $\large -\frac{125n}{8}+246=-4$ $\large -\frac{125n}{8}=-4-246$ $\large -\frac{125n}{8}=-250$ $\large -125n=-250*8$ $\large -125n=-2000$ $\large n=-\frac{2000}{-125}$ $\large n=16$

OpenStudy (anonymous):

thnk u jim

jimthompson5910 (jim_thompson5910):

np

OpenStudy (anonymous):

Solved with two Mathematica statements. Refer to the attachment.

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