Question

If `(2x^2-7x+9)/f(x) = (2x-3)` with a remainder of 3, what is `f(x)`?

Answer 1

`f(x) = x - 2`

Explanation:

When D is divided by d, quotient is q and remainder is r.

`D = dq + r \Rightarrow d = \frac{D - r}{q}`

`D = 2x^2 - 7x + 9`

`q = 2x - 3`

`r = 3`

`\Rightarrow f = d = \frac{2x^2-7x + 9 - 3}{2x - 3} = x -2`