Question

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

Answer 1

`(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)`