# F(x) = 2x^3-5x^2+7x-3 and g(x) = 2x-3. What is the quotient and remainder in the form q(x) + (r(x))/g(x)?

May 29, 2018

${x}^{2} - x + 5 + \frac{12}{2 x - 3}$

#### Explanation:

The question is asking you to divide the polynomials to get the form of $q \left(x\right) + \frac{r \left(x\right)}{g} \left(x\right)$.

It's like solving $2$ divided by $7$ to get $3 \frac{1}{2}$, except we're doing this with polynomials.

$f \left(x\right) = 2 {x}^{3} + 5 {x}^{2} + 7 x - 3 , g \left(x\right) = 2 x - 3$

$f \left(x\right)$ can't go into $g \left(x\right)$ because it's bigger, so $g \left(x\right)$ will go into $f \left(x\right)$