Question

How do find the quotient of `(10b^2 + b - 1)/(2b + 3)`?

Answer 1

`(10b^2+b-1)/(2b+3)=(10b^2+15b-14b-21+20)/(2b+3)`
`=(5b(2b+3)-7(2b+3)+20)/(2b+3)=(5b-7)+20/(2b+3)`
`:."quotient polynomial"=q(b)=5b-7`

Explanation:

Using synthetic division :

`diamond(10b^2+b-1)div(2b+3)`

We have , `p(b)=10b^2+b-1 and "divisor :"b=-3/2`

We take ,coefficients of `p(b) to 10,1,-1`

. `-3/2 |` `10color(white)(........)1color(white)(......)-1`
`ulcolor(white)(.......)|` `ul(0color(white)( .......)-15color(white)(......)21`
`color(white)(........)10color(white)(......)-14color(white)(......)color(violet)(ul|20|`
Hence ,

`(10b^2+b-1)=(b+3/2)(10b-14)+(20)`

`(10b^2+b-1)=1/2(2b+3)(10b-14)+(20)`

`(10b^2+b-1)=(2b+3)(5b-7)+(20)`

We can see that , quotient polynomial :

`q(b)=1/2(10b-14)=5b-7 and"the Remainder"=20`