Question

How do you use synthetic division to divide `(2x^3-x^2+5x-12) /(2x - 3)`?

Answer 1

Quotient is `x^2+x+4` and remainder is `0`.

Explanation:

`2x^3-x^2+5x-12`

=`2x^3-3x^2+2x^2-3x+8x-12`

=`x^2*(2x-3)+x*(2x-3)+4*(2x-3)`

=`(2x-3)*(x^2+x+4)`

Hence quotient is `x^2+x+4` and remainder is `0`.