Question

-6x^3+3x^2-4 divide 2x-3 remainder theorem

Answer 1

1. Multiply
`2x-3` by
`-3x^2` to get
`(2x-3)\cdot (-3x^2)=-6x^3+9x^2.`

2. Subtract
`-6x^3+9x^2` from the polynomial
`-6x^3+3x^2-4.` You obtain

`-6x^2-4.`

3. Multiply
`2x-3` by
`-3x:`

`(2x-3)\cdot (-3x)=-6x^2+9x`

and subtract it from the polynomial
`-6x^2-4.`

The result is
`-9x-4.`

4. Multiply
`2x-3` by
`-(9)/(2):`

`(2x-3)\cdot \left(-(9)/(2)\right)=-9x+(27)/(2)`

and subtract it from
`-9x-4.` The result is

`-4-(27)/(2)=-(35)/(2)=-17.5.`

5. After division you get

`-6x^3+3x^2-4=(2x-3)\cdot (-3x^2-3x-4.5)-17.5.`