Question

How do you divide `(8g^3-6g^2+3g+5)/(2g+3)`?

Answer 1

By the ordinary algorithm division or by Ruffini method as the divisor is of first degree
`Q(x)=4g^2-9g+15` and `R(x)=-40`

Explanation:

I prefer the ordinary algorithm division because it is of "universal use"
`8g^3-6g^2+3g+5-(2g+3)( **4g^2** )=-18g^2+3g+5` first partial quotient and remainder

`-18g^2+3g+5-(2g+3)( **-9g** )=30g+5` second partial quotient and remainder

`30g+5-(2g+3)( **15** )=-40` last quotient term and final remainder

the quotient is `Q(x)=4g^2-9g+15` the remainder is `R(x)= -40`