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

Nov 1, 2015

$f \left(x\right) = x - 2$

#### Explanation:

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

$D = \mathrm{dq} + r \setminus R i g h t a r r o w d = \setminus \frac{D - r}{q}$

$D = 2 {x}^{2} - 7 x + 9$

$q = 2 x - 3$

$r = 3$

$\setminus R i g h t a r r o w f = d = \setminus \frac{2 {x}^{2} - 7 x + 9 - 3}{2 x - 3} = x - 2$