1. Multiply [tex]2x-3[/tex] by [tex]-3x^2[/tex] to get [tex](2x-3)\cdot (-3x^2)=-6x^3+9x^2.[/tex]
2. Subtract [tex]-6x^3+9x^2[/tex] from the polynomial [tex]-6x^3+3x^2-4.[/tex] You obtain
[tex]-6x^2-4.[/tex]
3. Multiply [tex]2x-3[/tex] by [tex]-3x:[/tex]
[tex](2x-3)\cdot (-3x)=-6x^2+9x[/tex]
and subtract it from the polynomial [tex]-6x^2-4.[/tex]
The result is [tex]-9x-4.[/tex]
4. Multiply [tex]2x-3[/tex] by [tex]-\dfrac{9}{2}:[/tex]
[tex](2x-3)\cdot \left(-\dfrac{9}{2}\right)=-9x+\dfrac{27}{2}[/tex]
and subtract it from [tex]-9x-4.[/tex] The result is
[tex]-4-\dfrac{27}{2}=-\dfrac{35}{2}=-17.5.[/tex]
5. After division you get
[tex]-6x^3+3x^2-4=(2x-3)\cdot (-3x^2-3x-4.5)-17.5.[/tex]
