Question

How do you divide `(b^3+2b^2-15b+49)div(b+6)` using synthetic division?

Answer 1

`(b^3+2b^2-15b+49)=(b+6)(b^2-4b+9)+(-5)`

Explanation:

`(b^3+2b^2-15b+49)div(b+6)`

Using synthetic division :

We have , `p(b)=b^3+2b^2-15b+49 and "divisor : " b=-6`

We take ,coefficients of `p(b) to 1,2,-15,49`

`-6 |` `1color(white)(........)2color(white)(.......)-15color(white)(.......)49`
`ulcolor(white)(....)|` `ul(0color(white)( .....)-6color(white)(..........)24color(white)(...)-54`
`color(white)(......)1color(white)(......)-4color(white)(........)color(white)(..)9color(white)(.....)color(violet)(ul|-5|`
We can see that , quotient polynomial :

`q(b)=b^2-4b+9 and"the Remainder"=-5`

Hence ,

`(b^3+2b^2-15b+49)=(b+6)(b^2-4b+9)+(-5)`