Answer
$x^2-2x+2$
Work Step by Step
The picture below shows the result of $(
x^3-4x^2+6x-4
)\div(
x-2
)$ using synthetic division.
The numbers on the last row in the picture below are the coefficients of the quotient and the remainder. The left-most number is the coefficient of $
x^3
$ (leading term of dividend) divided by $
x
$ (leading term of divisor). Since $
x^3\div x=x^2
,$ then the left-most number is the coefficient of $
x^2
$ and the next numbers are the coefficients of $x$ in decreasing exponent (down to exponent $0$). The right-most number, on the other hand, represents the remainder. Hence, the quotient is
\begin{align*}
x^2-2x+2
.\end{align*}
