Question

How do you divide `(x^3+15x^2+45x-25)div(x+5)` using synthetic division?

Answer 1

`(x^3+15x^2+45x-25)/(x+5)=x^2+10x-5`

Explanation:

`(x^3+15x^2+45x-25)/(x+5)`

`=(x^2(x+5)+10x^2+45x-25)/(x+5)`

`=(x^2(x+5)+10x(x+5)-5x-25)/(x+5)`

`=(x^2cancel((x+5))+10xcancel((x+5))-5cancel((x+5)))/cancel((x+5))`

`=x^2+10x-5`

\0/ Here's our answer !

Answer 2

`(x^3+15x^2+45x-25)=(x+5)(x^2+10x-5 )+(0)`

Explanation:

`(x^3+15x^2+45x-25)div(x+5)`

Using synthetic division :

We have , `p(x)=(x^3+15x^2+45x-25) and "divisor : " x=-5`

We take ,coefficients of `p(x) to 1,15,45,-25`

`-5|` `1color(white)(.......)15color(white)(........)45color(white)(.....)-25`
`ulcolor(white)(....)|` `ul(0color(white)( ....)-5color(white)(....)-50color(white)(..........)25`
`color(white)(......)1color(white)(........)10color(white)(....)-5color(white)(..........)color(violet)(ul|0|`
We can see that , quotient polynomial :

`q(x)=x^2+10x-5 and"the Remainder"=0`

Hence ,

`(x^3+15x^2+45x-25)=(x+5)(x^2+10x-5 )+(0)`