# What polynomial yields a quotient of 2x-3 and a remainder of 3 when it divides 2x^2-7x+9?

Jun 22, 2018

$\left(x - 2\right)$.

#### Explanation:

We know that,

The Dividend=(The Divisor)(The Quotient)+The Remainder.

So, if the Divisor Polynomial is $p \left(x\right)$, then,

$\therefore \left(2 {x}^{2} - 7 x + 9\right) = \left(2 x - 3\right) \cdot p \left(x\right) + 3$.

$\therefore 2 {x}^{2} - 7 x + 9 - 3 = \left(2 x - 3\right) \cdot p \left(x\right)$,

$i . e . , 2 {x}^{2} - 7 x + 6 = \left(2 x - 3\right) \cdot p \left(x\right)$.

$\therefore p \left(x\right) = \frac{2 {x}^{2} - 7 x + 6}{2 x - 3}$,

$= \frac{\left(x - 2\right) \cancel{\left(2 x - 3\right)}}{\cancel{\left(2 x - 3\right)}}$.

$\Rightarrow \text{ The Divisor Poly. is } \left(x - 2\right)$.