How do you divide #(8v^5+43v^4+5v+20)div(v+4)# using synthetic division?

1 Answer
Aug 10, 2018

Answer:

#(8v^5+43v^4+5v+20)/(v+4)#=#(8v^4+11v^3-44v^2+176v-699)+2816/(v+4)#

Explanation:

#(8v^5+43v^4+5v+20)div(v+4)#

We can divide this polynomial by using synthetic division

We have , #p(v)=(8v^5+43v^4+0v^3+0v^2+5v+20)#

# and "divisor :"v=-4#

We take ,coefficients of #p(v) to 8,43,0,0,5,20#

#-4 |# #8color(white)(.......)43color(white)(.........)0color(white)(..........)0color(white)(..........)5color(white)(..........)20#
#ulcolor(white)(....)|# #ul(0color(white)(..)-32color(white)(...)-44color(white)(.....)176color(white)(..)-704color(white)(.....)2796#
#color(white)(......)8color(white)(.......)11color(white)(....)-44color(white)(.....)176color(white)(..)-699color(white)(...)color(white)(..)color(violet)(ul|2816|#
We can see that , quotient polynomial :

#q(v)=8v^4+11v^3-44v^2+176v-699 #

#and"the Remainder"=2816#

Hence ,

#(8v^5+43v^4+5v+20)/(v+4)=#

#(8v^4+11v^3-44v^2+176v-699)+2816/(v+4)#