Question

How do you divide `(x^3-8x+3)div(x+3)` using synthetic division?

Answer 1

`(x^3-8x+3)/(x+3)=x^2-3x+1`

Explanation:

`(x^3-8x+3)/(x+3)`

`=(x^2(x+3)-3x^2-8x+3)/(x+3)`

`=(x^2cancel((x+3))-3xcancel((x+3))+1cancel((x+3)))/cancel((x+3))`

`=x^2-3x+1`

\0/ Here's our answer !

Answer 2

`(x^3-8x+3)=(x+3)(x^2-3x+1 )+(0)`

Explanation:

`(x^3-8x+3)div(x+3)`

Using synthetic division :

We have , `p(x)=(x^3+0x^2-8x+3) and "divisor : " x=-3`

We take , coefficients of `p(x) to 1,0 ,-8,3`

`-3|` `1color(white)(........)0color(white)(......)-8color(white)(..........)3`
`ulcolor(white)(....)|` `ul(0color(white)( ....)-3color(white)(..........)9color(white)(......)-3`
`color(white)(......)1color(white)(......)-3color(white)(........)1color(white)(..........)color(violet)(ul|0|`
We can see that , quotient polynomial :

`q(x)=x^2-3x+1 and"the Remainder"=0`

Hence ,

`(x^3-8x+3)=(x+3)(x^2-3x+1 )+(0)`