Question

How do you find the remainder when `(2x^4+6x^3+5x-6) / (x+2)`?

Answer 1

We can use synthetic division to find remainder or
We can also use remainder theorem
Remainder `= -32`

Explanation:

`(2x^4+6x^3+5x-6)/(x+2)`
Use synthetic Division

`x^4" " " " " "x^3" " " " " "x^2" " " " " "x^1" " " " "x^0`
`2" " " " " "6" " " " " "0" " " " " "5" " "" " "-6" " "` trial divisor`=-2`
`underline( " " " " " "-4 " " "" " "-4" " " " " "8" " " " "" -26)`
`2 " " " " " " 2 " " " " ""-4 " " " " " "13 " " "" " "-32`

Remainder`=-32`

Also , we can use the remainder theorem
We will use `x=-2` in the dividend

Let `P(x)=2x^4+6x^3+5x-6`
Find `P(-2)`

`P(-2)=2*(-2)^4+6(-2)^3+5(-2)-6`

`P(-2)= -32" " "`and this is the remainder