Answer
$(x-2)$.
Work Step by Step
The dividend is $2x^2-7x+9$.
The quotient is $2x-3$.
The remainder is $3$.
The divisor is $= \frac{dividend -remainder}{quotient} $
Substitute all values.
The divisor is $= \frac{2x^2-7x+9 -3}{2x-3} $
Simplify.
The divisor is $= \frac{2x^2-7x+6}{2x-3} $
$\begin{matrix}
& x & -2 & & & \leftarrow &Quotient\\
&-- &-- &--&--& \\
2x-3) &2x^2&-7x&+6 & \\
& 2x^2 & -3x & & & \leftarrow &x(2x-3) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & -4x & +6 & & \\
& & -4x & +6 & & \leftarrow & -2(2x-3) \\
& & -- & -- & & \leftarrow & subtract \\
& & 0&0 & & \leftarrow & Remainder
\end{matrix}$
Hence, the divisor is $(x-2)$.
