First, we are going to divide [tex]-4q^2-22q+12[/tex] by the divisor, which is [tex]2q+1[/tex]
[tex]\frac{-4q^2}{2q}=-2q[/tex]
Then, multiply [tex]2q+1[/tex] by [tex]2q+1[/tex]
[tex]-4q^2-2q[/tex]
We are going to subtract [tex]-4q^2-2q[/tex] from [tex]-4q^2-22q+12[/tex] in order to get the new remainder.
So...
[tex]\frac{-4q^2-22q+12}{2q+1}=-2q+\frac{-20q+12}{2q+1}[/tex]
[tex]=-2q+\frac{-20q+12}{2q+1}[/tex]
That's our answer.
Have a nice day! :)
