Question

use synthetic division to find the quotient. $\frac{x^{3}-2x}{x - 2}$
$?x^{2}+x++\frac{}{x - 2}$

Explanation:

Step1: Identify divisor root

The divisor is $x-2$, so root $r=2$.

Step2: List dividend coefficients

Rewrite $x^3-2x$ as $x^3+0x^2-2x+0$, coefficients: $1, 0, -2, 0$.

Step3: Set up synthetic division

2 | 1   0   -2   0
        2    4   4
      1   2    2   4

Step4: Map to quotient form

The first 3 values are quotient coefficients, last is remainder.

Answer:

$1x^2 + 2x + 2 + \frac{4}{x-2}$
So the filled values are: $1$, $2$, $2$, $4$